Generating catalan path diagrams using ballot sequences in latex

Question

here is a pictures of a catalan path:

It is a lattice path in Z^2 starting a some point (a,b) and using the steps (1,1) and (1,-1). It can be decoded (knowing the starting point) as a ballot sequence 111-1-1.... where 1 corresponds to up(1,1) and -1 to down(1,-1). Is there a way using tex to just type the ballot sequence and get the corresponding catalan path?

You realize that not all of us are math people here. Can you explain what is happening and maybe add a simple code snippet for the axis so we don't need to bother with those? — percusse, Feb 05 '16 at 10:28

score 6 · Answer 1 · answered Feb 05 '16 at 10:51

A simple foreach can do it:

\documentclass[tikz,border=2mm]{standalone}

\begin{document}
\begin{tikzpicture}
\draw[->] (0,-1)--++(90:4);
\draw[->] (-1,0)--++(0:12);
\coordinate (aux) at (0,0);
\foreach \i in {1,-1,1,1,1,-1,1,-1,-1,1,-1}
    \draw[->] (aux)--++(1,\i) coordinate (aux);
\end{tikzpicture}
\end{document}

score 3 · Answer 2 · answered Feb 09 '16 at 07:43

Just about does it (although without the axes):

\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{decorations.pathreplacing}
\tikzset{arrow path/.style={decoration={show path construction,
  lineto code={
    \path [->, every lineto/.try] 
      (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);
  }}, decorate},
  every lineto/.style={draw, thick, ->},
  lineto/.style={every lineto/.append style={#1}},
  ballot sequence/.style={arrow path, .. ballot sequence=#1@@;},
  .. ballot sequence/.code args={#1#2#3;}{%
    \if#1@\else
      \if#1-
      \tikzset{symbol #1#2/.try, .. ballot sequence=#3;}%
    \else
      \tikzset{symbol #1/.try, .. ballot sequence=#2#3;}%
    \fi\fi%
  },
  symbol -1/.style={insert path={ -- ++(1,-1) }},
  symbol 1/.style={insert path={ -- ++(1,1) }}
}
\begin{document} 
\begin{tikzpicture}[>=stealth]
\path [lineto=red]   (5,0) [ballot sequence={1-1}];
\path [lineto=green] (3,3) [ballot sequence={111-1-1-1}];
\path [lineto=blue]  (0,6) [ballot sequence={1-1111-11-1-11-1-1}];
\end{tikzpicture}
\end{document}

Generating catalan path diagrams using ballot sequences in latex

2 Answers2