Example: Plane partition

Published 2009-08-17 | Author: Jang Soo Kim

Illustration of a plane partition.

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Plane partition

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% Plane partition
% Author: Jang Soo Kim
\documentclass{minimal}
\usepackage{tikz}
% Three counters
\newcounter{x}
\newcounter{y}
\newcounter{z}

% The angles of x,y,z-axes
\newcommand\xaxis{210}
\newcommand\yaxis{-30}
\newcommand\zaxis{90}

% The top side of a cube
\newcommand\topside[3]{
  \fill[fill=yellow, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (30:1) -- (0,1) --(150:1)--(0,0);
}

% The left side of a cube
\newcommand\leftside[3]{
  \fill[fill=red, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (0,-1) -- (210:1) --(150:1)--(0,0);
}

% The right side of a cube
\newcommand\rightside[3]{
  \fill[fill=blue, draw=black,shift={(\xaxis:#1)},shift={(\yaxis:#2)},
  shift={(\zaxis:#3)}] (0,0) -- (30:1) -- (-30:1) --(0,-1)--(0,0);
}

% The cube 
\newcommand\cube[3]{
  \topside{#1}{#2}{#3} \leftside{#1}{#2}{#3} \rightside{#1}{#2}{#3}
}

% Definition of \planepartition
% To draw the following plane partition, just write \planepartition{ {a, b, c}, {d,e} }.
%  a b c
%  d e
\newcommand\planepartition[1]{
 \setcounter{x}{-1}
  \foreach \a in {#1} {
    \addtocounter{x}{1}
    \setcounter{y}{-1}
    \foreach \b in \a {
      \addtocounter{y}{1}
      \setcounter{z}{-1}
      \foreach \c in {1,...,\b} {
        \addtocounter{z}{1}
        \cube{\value{x}}{\value{y}}{\value{z}}
      }
    }
  }
}

\begin{document} 

\begin{tikzpicture}
\planepartition{{5,3,2,2},{4,2,2,1},{2,1},{1}}
\end{tikzpicture}

\end{document} 

Comments

  • #1 Dick van der Leeden, April 4, 2010 at 3:16 p.m.

    Great work!

    I noticed however that a zero in the definition, such as

    \planepartition{{5,3,0,2},{4,2,2,1},{2,1},{1}}
    

    results in a stack of 2 cubes in stead of no cubes!

    Is it possible to fix this?

    Thanks, Dick

  • #2 Dick van der Leeden, April 4, 2010 at 8:39 p.m.

    I guess I found a solution myself, here is the new definition of \planepartition

    \newcommand\planepartition[1]{
     \setcounter{x}{-1}
      \foreach \a in {#1} {
        \addtocounter{x}{1}
        \setcounter{y}{-1}
        \foreach \b in \a {
          \addtocounter{y}{1}
          \setcounter{z}{-1}
          \foreach \c in {0,...,\b} {
            \addtocounter{z}{1}
          \ifthenelse{\c=0}{\setcounter{z}{-1},\addtocounter{y}{0}}{
            \cube{\value{x}}{\value{y}}{\value{z}}}
          }
        }
      }
    }
    
  • #3 Vin, October 8, 2010 at 3:49 a.m.

    Jang Soo Kim's programme is impressive.

    Dick's work makes it prefect.

    Is the part "\addtocounter{y}{0}" necessary in the ifthenelse statement?

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