Dyck paths with extra diagonals from valleys (Laser construction)Drawing paths with TikZ from a DB with DataToolconstruction set of treeTikZ reusable paths with variablesNumerical conditional within tikz keys?How to draw points in TikZ?Line up nested tikz enviroments or how to get rid of themHow to draw a square and its diagonals with arrows?Help needed with drawing diagonals over the pageHow to split a (Hobby) path in twoIntersection between paths from different axis environments
What term is being referred to with "reflected-sound-of-underground-spirits"?
Check if a string is entirely made of the same substring
What is the most expensive material in the world that could be used to create Pun-Pun's lute?
As an international instructor, should I openly talk about my accent?
Why did C use the -> operator instead of reusing the . operator?
Why does Mind Blank stop the Feeblemind spell?
Was Dennis Ritchie being too modest in this quote about C and Pascal?
How did Captain America manage to do this?
How to write a column outside the braces in a matrix?
Contradiction proof for inequality of P and NP?
Why was the Spitfire's elliptical wing almost uncopied by other aircraft of World War 2?
Can I criticise the more senior developers around me for not writing clean code?
If a planet has 3 moons, is it possible to have triple Full/New Moons at once?
How can Republicans who favour free markets, consistently express anger when they don't like the outcome of that choice?
Which big number is bigger?
Dynamic SOQL query relationship with field visibility for Users
How to limit Drive Letters Windows assigns to new removable USB drives
How can I practically buy stocks?
Solving polynominals equations (relationship of roots)
What happens to Mjolnir (Thor's hammer) at the end of Endgame?
How to pronounce 'c++' in Spanish
Phrase for the opposite of "foolproof"
Checks user level and limit the data before saving it to mongoDB
"The cow" OR "a cow" OR "cows" in this context
Dyck paths with extra diagonals from valleys (Laser construction)
Drawing paths with TikZ from a DB with DataToolconstruction set of treeTikZ reusable paths with variablesNumerical conditional within tikz keys?How to draw points in TikZ?Line up nested tikz enviroments or how to get rid of themHow to draw a square and its diagonals with arrows?Help needed with drawing diagonals over the pageHow to split a (Hobby) path in twoIntersection between paths from different axis environments
I would like to create a Dyck path in Latex with two additional features. First, I would like to number all the East step except(!) for the last one. Secondly, for each valley (that is, an East step that is followed by a North step), I would like to draw "lasers" which would be lines that are parallel to the diagonal and that stops once it reaches the Dyck path. This is similar, but not exactly the same as the "laser construction" in this paper. See e.g. Figure 6.
I already have some code to obtain a Dyck path.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,1,0,0,0,1,0,1,0;
endtikzpicture
enddocument
which produces the following picture.
Whereas I would like to obtain something like
Is it be possible to modify my existing code to obtain what I desire? If not, is there an alternative approach?
tikz-pgf
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
add a comment |
I would like to create a Dyck path in Latex with two additional features. First, I would like to number all the East step except(!) for the last one. Secondly, for each valley (that is, an East step that is followed by a North step), I would like to draw "lasers" which would be lines that are parallel to the diagonal and that stops once it reaches the Dyck path. This is similar, but not exactly the same as the "laser construction" in this paper. See e.g. Figure 6.
I already have some code to obtain a Dyck path.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,1,0,0,0,1,0,1,0;
endtikzpicture
enddocument
which produces the following picture.
Whereas I would like to obtain something like
Is it be possible to modify my existing code to obtain what I desire? If not, is there an alternative approach?
tikz-pgf
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
1
What I mean is that you can add the lines "by hand" inside thetikzpicture
– JouleV
Apr 19 at 15:02
add a comment |
I would like to create a Dyck path in Latex with two additional features. First, I would like to number all the East step except(!) for the last one. Secondly, for each valley (that is, an East step that is followed by a North step), I would like to draw "lasers" which would be lines that are parallel to the diagonal and that stops once it reaches the Dyck path. This is similar, but not exactly the same as the "laser construction" in this paper. See e.g. Figure 6.
I already have some code to obtain a Dyck path.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,1,0,0,0,1,0,1,0;
endtikzpicture
enddocument
which produces the following picture.
Whereas I would like to obtain something like
Is it be possible to modify my existing code to obtain what I desire? If not, is there an alternative approach?
tikz-pgf
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
I would like to create a Dyck path in Latex with two additional features. First, I would like to number all the East step except(!) for the last one. Secondly, for each valley (that is, an East step that is followed by a North step), I would like to draw "lasers" which would be lines that are parallel to the diagonal and that stops once it reaches the Dyck path. This is similar, but not exactly the same as the "laser construction" in this paper. See e.g. Figure 6.
I already have some code to obtain a Dyck path.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,1,0,0,0,1,0,1,0;
endtikzpicture
enddocument
which produces the following picture.
Whereas I would like to obtain something like
Is it be possible to modify my existing code to obtain what I desire? If not, is there an alternative approach?
tikz-pgf
tikz-pgf
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
asked Apr 19 at 14:38
Joakim UhlinJoakim Uhlin
1347
1347
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
1
What I mean is that you can add the lines "by hand" inside thetikzpicture
– JouleV
Apr 19 at 15:02
add a comment |
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
1
What I mean is that you can add the lines "by hand" inside thetikzpicture
– JouleV
Apr 19 at 15:02
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
1
1
What I mean is that you can add the lines "by hand" inside the
tikzpicture– JouleV
Apr 19 at 15:02
What I mean is that you can add the lines "by hand" inside the
tikzpicture– JouleV
Apr 19 at 15:02
add a comment |
3 Answers
3
active
oldest
votes
Just for fun, something that adds the numbers and laser lines automatically. The laser lines are drawn automatically according to your clarified prescription. The strategy is to look at the elements of the list that are ahead and check whether or not they fulfill certain criteria. The integer vtest tests if the current point is a "valley", in which case it is 10, and the other integers are constructed similarly.
documentclass[tikz,border=3.14mm]standalone
newcounterDyckHsteps
begindocument
tikzsetcount list/.code 2 args=foreach XX [count=YY] in #1
xdef#2YY,Dyck arrow/.style=ultra thick,-stealth,
laser/.style=draw=blue,
Dyck path/.style=count list=#1DyckSteps,
/utils/exec=setcounterDyckHsteps0,insert path=%
foreach XX [count=YY,remember=YY as LastY (initially 0)]in #1
ifnumXX=0
edge[Dyck arrow] ++(1,0) ++(1,0) coordinate(Dyck-YY)
ifnumYY<DyckSteps
(Dyck-LastY) -- (Dyck-YY) node[midway,above]stepcounterDyckHstepsnumbervalueDyckHsteps
fi
else
edge[Dyck arrow] ++(0,1) ++(0,1) coordinate(Dyck-YY)
fi
pgfextrapgfmathtruncatemacrovtest0pgfmathtruncatemacroftest0pgfmathtruncatemacrohtest0pgfmathtruncatemacroitest1
pgfmathtruncatemacroRestStepsDyckSteps-YY
ifnumYY>1
ifnumRestSteps>1
pgfmathtruncatemacroftest#1[YY+1]+#1[YY]*10 % should be 10
pgfmathtruncatemacrovtest#1[YY-1]+10*#1[YY] % valley test
fi
ifnumRestSteps>3
pgfmathtruncatemacrohtestpow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0))
fi
ifnumRestSteps>5
pgfmathtruncatemacroitestpow(-1,#1[YY+5])+
pow(-1,#1[YY+4])+pow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0)
+ifthenelse(#1[YY-2]==1,11,0)
fi
fi%typeoutYY:RestSteps:ftest,htest,itest,vtest
ifnumvtest=10
%(Dyck-YY) node[blue,fill,circle,inner sep=2pt](Dyck-YY)
ifnumitest=0
(Dyck-YY) edge[laser] ++(3,3) (Dyck-YY)
fi
ifnumhtest=1100
(Dyck-YY) edge[laser] ++(-2,-2) (Dyck-YY)
fi
ifnumftest=10
(Dyck-YY) edge[laser] ++(1,1) (Dyck-YY)
fi
fi
begintikzpicture
draw (0,0) grid (6,6);
draw (0,0) [Dyck path=1,1,0,1,0,0,1,1,0,1,0,0];
endtikzpicture
enddocument
answered Apr 19 at 16:55
marmotmarmot
121k6159297
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
|
show 5 more comments
With the help from JouleV, I managed to do solve this but I am leaving this as an answer for people who might be interested.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node at (0.5, 2.5) 1;
node at (1.5, 3.5) 2;
node at (2.5, 3.5) 3;
node at (3.5, 5.5) 4;
node at (4.5, 6.5) 5;
endtikzpicture
enddocument
This produces the following the picture
Perhaps not the most pretty solution and quite mechanical but it works for my purposes. However, It would still be interesting to have a more general solution so that I would not need to draw lines and numbers manually.
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
add a comment |
First, congratulations for figuring out everything by yourself. I upvoted your answer.
This answer is a slight improvement of your answer in the position of the nodes (the numbers). I use option above to have a better space between the number and the line below it.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node[above=2pt] at (0.5, 2) 1;
node[above=2pt] at (1.5, 3) 2;
node[above=2pt] at (2.5, 3) 3;
node[above=2pt] at (3.5, 5) 4;
node[above=2pt] at (4.5, 6) 5;
endtikzpicture
enddocument
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "85"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f485606%2fdyck-paths-with-extra-diagonals-from-valleys-laser-construction%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Just for fun, something that adds the numbers and laser lines automatically. The laser lines are drawn automatically according to your clarified prescription. The strategy is to look at the elements of the list that are ahead and check whether or not they fulfill certain criteria. The integer vtest tests if the current point is a "valley", in which case it is 10, and the other integers are constructed similarly.
documentclass[tikz,border=3.14mm]standalone
newcounterDyckHsteps
begindocument
tikzsetcount list/.code 2 args=foreach XX [count=YY] in #1
xdef#2YY,Dyck arrow/.style=ultra thick,-stealth,
laser/.style=draw=blue,
Dyck path/.style=count list=#1DyckSteps,
/utils/exec=setcounterDyckHsteps0,insert path=%
foreach XX [count=YY,remember=YY as LastY (initially 0)]in #1
ifnumXX=0
edge[Dyck arrow] ++(1,0) ++(1,0) coordinate(Dyck-YY)
ifnumYY<DyckSteps
(Dyck-LastY) -- (Dyck-YY) node[midway,above]stepcounterDyckHstepsnumbervalueDyckHsteps
fi
else
edge[Dyck arrow] ++(0,1) ++(0,1) coordinate(Dyck-YY)
fi
pgfextrapgfmathtruncatemacrovtest0pgfmathtruncatemacroftest0pgfmathtruncatemacrohtest0pgfmathtruncatemacroitest1
pgfmathtruncatemacroRestStepsDyckSteps-YY
ifnumYY>1
ifnumRestSteps>1
pgfmathtruncatemacroftest#1[YY+1]+#1[YY]*10 % should be 10
pgfmathtruncatemacrovtest#1[YY-1]+10*#1[YY] % valley test
fi
ifnumRestSteps>3
pgfmathtruncatemacrohtestpow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0))
fi
ifnumRestSteps>5
pgfmathtruncatemacroitestpow(-1,#1[YY+5])+
pow(-1,#1[YY+4])+pow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0)
+ifthenelse(#1[YY-2]==1,11,0)
fi
fi%typeoutYY:RestSteps:ftest,htest,itest,vtest
ifnumvtest=10
%(Dyck-YY) node[blue,fill,circle,inner sep=2pt](Dyck-YY)
ifnumitest=0
(Dyck-YY) edge[laser] ++(3,3) (Dyck-YY)
fi
ifnumhtest=1100
(Dyck-YY) edge[laser] ++(-2,-2) (Dyck-YY)
fi
ifnumftest=10
(Dyck-YY) edge[laser] ++(1,1) (Dyck-YY)
fi
fi
begintikzpicture
draw (0,0) grid (6,6);
draw (0,0) [Dyck path=1,1,0,1,0,0,1,1,0,1,0,0];
endtikzpicture
enddocument
answered Apr 19 at 16:55
marmotmarmot
121k6159297
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
|
show 5 more comments
Just for fun, something that adds the numbers and laser lines automatically. The laser lines are drawn automatically according to your clarified prescription. The strategy is to look at the elements of the list that are ahead and check whether or not they fulfill certain criteria. The integer vtest tests if the current point is a "valley", in which case it is 10, and the other integers are constructed similarly.
documentclass[tikz,border=3.14mm]standalone
newcounterDyckHsteps
begindocument
tikzsetcount list/.code 2 args=foreach XX [count=YY] in #1
xdef#2YY,Dyck arrow/.style=ultra thick,-stealth,
laser/.style=draw=blue,
Dyck path/.style=count list=#1DyckSteps,
/utils/exec=setcounterDyckHsteps0,insert path=%
foreach XX [count=YY,remember=YY as LastY (initially 0)]in #1
ifnumXX=0
edge[Dyck arrow] ++(1,0) ++(1,0) coordinate(Dyck-YY)
ifnumYY<DyckSteps
(Dyck-LastY) -- (Dyck-YY) node[midway,above]stepcounterDyckHstepsnumbervalueDyckHsteps
fi
else
edge[Dyck arrow] ++(0,1) ++(0,1) coordinate(Dyck-YY)
fi
pgfextrapgfmathtruncatemacrovtest0pgfmathtruncatemacroftest0pgfmathtruncatemacrohtest0pgfmathtruncatemacroitest1
pgfmathtruncatemacroRestStepsDyckSteps-YY
ifnumYY>1
ifnumRestSteps>1
pgfmathtruncatemacroftest#1[YY+1]+#1[YY]*10 % should be 10
pgfmathtruncatemacrovtest#1[YY-1]+10*#1[YY] % valley test
fi
ifnumRestSteps>3
pgfmathtruncatemacrohtestpow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0))
fi
ifnumRestSteps>5
pgfmathtruncatemacroitestpow(-1,#1[YY+5])+
pow(-1,#1[YY+4])+pow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0)
+ifthenelse(#1[YY-2]==1,11,0)
fi
fi%typeoutYY:RestSteps:ftest,htest,itest,vtest
ifnumvtest=10
%(Dyck-YY) node[blue,fill,circle,inner sep=2pt](Dyck-YY)
ifnumitest=0
(Dyck-YY) edge[laser] ++(3,3) (Dyck-YY)
fi
ifnumhtest=1100
(Dyck-YY) edge[laser] ++(-2,-2) (Dyck-YY)
fi
ifnumftest=10
(Dyck-YY) edge[laser] ++(1,1) (Dyck-YY)
fi
fi
begintikzpicture
draw (0,0) grid (6,6);
draw (0,0) [Dyck path=1,1,0,1,0,0,1,1,0,1,0,0];
endtikzpicture
enddocument
answered Apr 19 at 16:55
marmotmarmot
121k6159297
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
|
show 5 more comments
Just for fun, something that adds the numbers and laser lines automatically. The laser lines are drawn automatically according to your clarified prescription. The strategy is to look at the elements of the list that are ahead and check whether or not they fulfill certain criteria. The integer vtest tests if the current point is a "valley", in which case it is 10, and the other integers are constructed similarly.
documentclass[tikz,border=3.14mm]standalone
newcounterDyckHsteps
begindocument
tikzsetcount list/.code 2 args=foreach XX [count=YY] in #1
xdef#2YY,Dyck arrow/.style=ultra thick,-stealth,
laser/.style=draw=blue,
Dyck path/.style=count list=#1DyckSteps,
/utils/exec=setcounterDyckHsteps0,insert path=%
foreach XX [count=YY,remember=YY as LastY (initially 0)]in #1
ifnumXX=0
edge[Dyck arrow] ++(1,0) ++(1,0) coordinate(Dyck-YY)
ifnumYY<DyckSteps
(Dyck-LastY) -- (Dyck-YY) node[midway,above]stepcounterDyckHstepsnumbervalueDyckHsteps
fi
else
edge[Dyck arrow] ++(0,1) ++(0,1) coordinate(Dyck-YY)
fi
pgfextrapgfmathtruncatemacrovtest0pgfmathtruncatemacroftest0pgfmathtruncatemacrohtest0pgfmathtruncatemacroitest1
pgfmathtruncatemacroRestStepsDyckSteps-YY
ifnumYY>1
ifnumRestSteps>1
pgfmathtruncatemacroftest#1[YY+1]+#1[YY]*10 % should be 10
pgfmathtruncatemacrovtest#1[YY-1]+10*#1[YY] % valley test
fi
ifnumRestSteps>3
pgfmathtruncatemacrohtestpow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0))
fi
ifnumRestSteps>5
pgfmathtruncatemacroitestpow(-1,#1[YY+5])+
pow(-1,#1[YY+4])+pow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0)
+ifthenelse(#1[YY-2]==1,11,0)
fi
fi%typeoutYY:RestSteps:ftest,htest,itest,vtest
ifnumvtest=10
%(Dyck-YY) node[blue,fill,circle,inner sep=2pt](Dyck-YY)
ifnumitest=0
(Dyck-YY) edge[laser] ++(3,3) (Dyck-YY)
fi
ifnumhtest=1100
(Dyck-YY) edge[laser] ++(-2,-2) (Dyck-YY)
fi
ifnumftest=10
(Dyck-YY) edge[laser] ++(1,1) (Dyck-YY)
fi
fi
begintikzpicture
draw (0,0) grid (6,6);
draw (0,0) [Dyck path=1,1,0,1,0,0,1,1,0,1,0,0];
endtikzpicture
enddocument
answered Apr 19 at 16:55
marmotmarmot
121k6159297
Just for fun, something that adds the numbers and laser lines automatically. The laser lines are drawn automatically according to your clarified prescription. The strategy is to look at the elements of the list that are ahead and check whether or not they fulfill certain criteria. The integer vtest tests if the current point is a "valley", in which case it is 10, and the other integers are constructed similarly.
documentclass[tikz,border=3.14mm]standalone
newcounterDyckHsteps
begindocument
tikzsetcount list/.code 2 args=foreach XX [count=YY] in #1
xdef#2YY,Dyck arrow/.style=ultra thick,-stealth,
laser/.style=draw=blue,
Dyck path/.style=count list=#1DyckSteps,
/utils/exec=setcounterDyckHsteps0,insert path=%
foreach XX [count=YY,remember=YY as LastY (initially 0)]in #1
ifnumXX=0
edge[Dyck arrow] ++(1,0) ++(1,0) coordinate(Dyck-YY)
ifnumYY<DyckSteps
(Dyck-LastY) -- (Dyck-YY) node[midway,above]stepcounterDyckHstepsnumbervalueDyckHsteps
fi
else
edge[Dyck arrow] ++(0,1) ++(0,1) coordinate(Dyck-YY)
fi
pgfextrapgfmathtruncatemacrovtest0pgfmathtruncatemacroftest0pgfmathtruncatemacrohtest0pgfmathtruncatemacroitest1
pgfmathtruncatemacroRestStepsDyckSteps-YY
ifnumYY>1
ifnumRestSteps>1
pgfmathtruncatemacroftest#1[YY+1]+#1[YY]*10 % should be 10
pgfmathtruncatemacrovtest#1[YY-1]+10*#1[YY] % valley test
fi
ifnumRestSteps>3
pgfmathtruncatemacrohtestpow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0))
fi
ifnumRestSteps>5
pgfmathtruncatemacroitestpow(-1,#1[YY+5])+
pow(-1,#1[YY+4])+pow(-1,#1[YY+3])+pow(-1,#1[YY+2])
+pow(-1,#1[YY+1])+pow(-1,#1[YY])+ifthenelse(#1[YY-1]==1,11,0)
+ifthenelse(#1[YY-2]==1,11,0)
fi
fi%typeoutYY:RestSteps:ftest,htest,itest,vtest
ifnumvtest=10
%(Dyck-YY) node[blue,fill,circle,inner sep=2pt](Dyck-YY)
ifnumitest=0
(Dyck-YY) edge[laser] ++(3,3) (Dyck-YY)
fi
ifnumhtest=1100
(Dyck-YY) edge[laser] ++(-2,-2) (Dyck-YY)
fi
ifnumftest=10
(Dyck-YY) edge[laser] ++(1,1) (Dyck-YY)
fi
fi
begintikzpicture
draw (0,0) grid (6,6);
draw (0,0) [Dyck path=1,1,0,1,0,0,1,1,0,1,0,0];
endtikzpicture
enddocument
answered Apr 19 at 16:55
marmotmarmot
121k6159297
edited Apr 19 at 18:16
answered Apr 19 at 16:55
marmotmarmot
121k6159297
answered Apr 19 at 16:55
marmotmarmot
121k6159297
answered Apr 19 at 16:55
marmotmarmot
121k6159297
121k6159297
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
|
show 5 more comments
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
Nice! But (at least in my case) the lasers should only go from the valleys and up-right. I imagine one could modify the code to get this tho.
– Joakim Uhlin
Apr 19 at 17:06
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
@JoakimUhlin They go right-up, don't they?
– marmot
Apr 19 at 17:08
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
True but they also go down-left in your case. You can compare this to my picture. For example, there should not be a laser between (0,0) and (3,3) but there should be one between (3,3) and (6,6).
– Joakim Uhlin
Apr 19 at 17:12
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
@JoakimUhlin Hmm, sorry, I do not understand these prescriptions. Whether it is up-right or down-left is only a matter of perspective, isn't it? From the point (0,0) you can go up-right to (3,3), or you can go from (3,3) down-left to (0,0), the result looks identical to me.
– marmot
Apr 19 at 17:16
1
1
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
@JoakimUhlin I updated the answer accordingly.
– marmot
Apr 19 at 18:16
|
show 5 more comments
With the help from JouleV, I managed to do solve this but I am leaving this as an answer for people who might be interested.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node at (0.5, 2.5) 1;
node at (1.5, 3.5) 2;
node at (2.5, 3.5) 3;
node at (3.5, 5.5) 4;
node at (4.5, 6.5) 5;
endtikzpicture
enddocument
This produces the following the picture
Perhaps not the most pretty solution and quite mechanical but it works for my purposes. However, It would still be interesting to have a more general solution so that I would not need to draw lines and numbers manually.
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
add a comment |
With the help from JouleV, I managed to do solve this but I am leaving this as an answer for people who might be interested.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node at (0.5, 2.5) 1;
node at (1.5, 3.5) 2;
node at (2.5, 3.5) 3;
node at (3.5, 5.5) 4;
node at (4.5, 6.5) 5;
endtikzpicture
enddocument
This produces the following the picture
Perhaps not the most pretty solution and quite mechanical but it works for my purposes. However, It would still be interesting to have a more general solution so that I would not need to draw lines and numbers manually.
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
add a comment |
With the help from JouleV, I managed to do solve this but I am leaving this as an answer for people who might be interested.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node at (0.5, 2.5) 1;
node at (1.5, 3.5) 2;
node at (2.5, 3.5) 3;
node at (3.5, 5.5) 4;
node at (4.5, 6.5) 5;
endtikzpicture
enddocument
This produces the following the picture
Perhaps not the most pretty solution and quite mechanical but it works for my purposes. However, It would still be interesting to have a more general solution so that I would not need to draw lines and numbers manually.
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
With the help from JouleV, I managed to do solve this but I am leaving this as an answer for people who might be interested.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node at (0.5, 2.5) 1;
node at (1.5, 3.5) 2;
node at (2.5, 3.5) 3;
node at (3.5, 5.5) 4;
node at (4.5, 6.5) 5;
endtikzpicture
enddocument
This produces the following the picture
Perhaps not the most pretty solution and quite mechanical but it works for my purposes. However, It would still be interesting to have a more general solution so that I would not need to draw lines and numbers manually.
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
answered Apr 19 at 15:24
Joakim UhlinJoakim Uhlin
1347
1347
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
add a comment |
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
1
1
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
I think this is going to be the most general solution unless someone comes up with a tikz package for drawing your specific kind of graph/path.
– nomen
Apr 19 at 22:22
add a comment |
First, congratulations for figuring out everything by yourself. I upvoted your answer.
This answer is a slight improvement of your answer in the position of the nodes (the numbers). I use option above to have a better space between the number and the line below it.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node[above=2pt] at (0.5, 2) 1;
node[above=2pt] at (1.5, 3) 2;
node[above=2pt] at (2.5, 3) 3;
node[above=2pt] at (3.5, 5) 4;
node[above=2pt] at (4.5, 6) 5;
endtikzpicture
enddocument
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
add a comment |
First, congratulations for figuring out everything by yourself. I upvoted your answer.
This answer is a slight improvement of your answer in the position of the nodes (the numbers). I use option above to have a better space between the number and the line below it.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node[above=2pt] at (0.5, 2) 1;
node[above=2pt] at (1.5, 3) 2;
node[above=2pt] at (2.5, 3) 3;
node[above=2pt] at (3.5, 5) 4;
node[above=2pt] at (4.5, 6) 5;
endtikzpicture
enddocument
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
add a comment |
First, congratulations for figuring out everything by yourself. I upvoted your answer.
This answer is a slight improvement of your answer in the position of the nodes (the numbers). I use option above to have a better space between the number and the line below it.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node[above=2pt] at (0.5, 2) 1;
node[above=2pt] at (1.5, 3) 2;
node[above=2pt] at (2.5, 3) 3;
node[above=2pt] at (3.5, 5) 4;
node[above=2pt] at (4.5, 6) 5;
endtikzpicture
enddocument
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
First, congratulations for figuring out everything by yourself. I upvoted your answer.
This answer is a slight improvement of your answer in the position of the nodes (the numbers). I use option above to have a better space between the number and the line below it.
documentclassarticle
usepackagetikz
newcommandNEpath[4]
fill[white!25] (#1) rectangle +(#2,#3);
fill[fill=white]
(#1)
foreach dir in #4
ifnumdir=0
-- ++(1,0)
else
-- ++(0,1)
fi
begindocument
begintikzpicture
NEpath0,0661,1,0,1,0,0,1,1,0,1,0,0;
draw (1,2) -- +(1,1);
draw (3,3.1) -- +(2.9,2.9);
draw (4,5) -- +(1,1);
node[above=2pt] at (0.5, 2) 1;
node[above=2pt] at (1.5, 3) 2;
node[above=2pt] at (2.5, 3) 3;
node[above=2pt] at (3.5, 5) 4;
node[above=2pt] at (4.5, 6) 5;
endtikzpicture
enddocument
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
answered Apr 19 at 15:30
JouleVJouleV
16.1k22667
16.1k22667
add a comment |
add a comment |
Thanks for contributing an answer to TeX - LaTeX Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2ftex.stackexchange.com%2fquestions%2f485606%2fdyck-paths-with-extra-diagonals-from-valleys-laser-construction%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
How about adding those paths manually?
– JouleV
Apr 19 at 14:41
Btw, as it is an arXiv document, you may find the source code of the file, thus you can find the code for the picture
– JouleV
Apr 19 at 14:42
@JouleV I am unfortunately not very good with tikz - what do you mean by adding the paths manually? Also, the image in the pdf is not done in tikz but rather attached as a pdf.
– Joakim Uhlin
Apr 19 at 14:59
1
What I mean is that you can add the lines "by hand" inside the
tikzpicture– JouleV
Apr 19 at 15:02