How can I typeset this correspondence in LaTeX?

Question

I am looking to create a "table" or something similar in LaTeX where I show correspondence/mapping between a natural number and some other natural number, as indicated in the picture below (please excuse the badly drawn Paint example):

In other words "one maps onto zero, two maps onto one..." etc. I am, however, not sure how to do so in LaTeX.

Can anyone please provide me with some help as to how I can go about typesetting something similar to this in a LaTeX environment?

Answer 1

One option using a matrix; an array could also be used, but with matrix you don't have to specify the number and format of columns:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\begin{matrix}
0 & 1 & 2 \\
\updownarrow & \updownarrow & \updownarrow  \\
2 & 3 & 1 
\end{matrix}
\]

\end{document}

As has been noted, the vertical space around the arrows seems a little uneven: there's more space above the arrows than below them, so one can easily fix it:

\documentclass{article}
\usepackage{amsmath}

\newcommand\UpDownarrow[1][0.2ex]{
  \raisebox{#1}[0pt][0pt]{$\updownarrow$}
}

\begin{document}
\[
\begin{matrix}
0 & 1 & 2 \\
\UpDownarrow & \UpDownarrow & \UpDownarrow \\
2 & 3 & 1 
\end{matrix}
\]

\end{document}

Just for the record, the array version:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\begin{array}{ccc}
0 & 1 & 2 \\
\updownarrow & \updownarrow & \updownarrow  \\
2 & 3 & 1 
\end{array}
\]

\end{document}

Answer 2

This might seem an overkill, but may be a good way of generalization.

\documentclass{scrartcl}
\usepackage{mathtools,tikz}
\usetikzlibrary{matrix}

\begin{document}
\[
  \begin{tikzpicture}
    \matrix[name=m,matrix of math nodes,column sep=1em,row sep=1em]
      {0 & 1 & 2 \\ 2 & 3 & 1 \\};
    \draw[<->] (m-1-1) -- (m-2-1);
    \draw[<->] (m-1-2) -- (m-2-2);
    \draw[<->] (m-1-3) -- (m-2-3);
  \end{tikzpicture}
\]
\end{document}

P.S.: If you load \usetikzlibrary{arrows.meta} it will probably give better arrowheads by default.

Answer 3

Yet another tikz solution, but here I use a \foreach loop:

\documentclass{article}
\usepackage{tikz}
\newcommand\aestrut{\rule[-0.5ex]{0pt}{2ex}}
\begin{document}

  \begin{tikzpicture}[my node/.style={anchor=base}]
    \foreach[count=\myi from 0] \mya/\myb in {0/1,1/2,2/3,h/g,e/j,j/k}
    {
      \node[my node] (A\myi) at (\myi,1) {\aestrut\mya};
      \node[my node] (B\myi) at (\myi,0) {\aestrut\myb};
      \draw[arrows=<->] (A\myi) -- (B\myi);
    }
  \end{tikzpicture}

\end{document}

It is a bit to set up, but once it's been set up it's very easy to add or remove pairs from the correspondence: just add (or remove) the pair from the in {.....} group where the pairs are separated by /.

Answer 4

Depending on your intended use, a TABstack may offer certain advantages.

\documentclass{article}
\usepackage{amsmath,tabstackengine,xcolor}
\stackMath
\begin{document}
While a TABstack can be used in a math environment
\[
\tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1}
\]
it can also be used inline: 
\tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1}
\\with differing vertical alignments
\tabbedLongstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1} 
or 
\tabbedLongunderstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1},\\
with different horizontal gap%
\setstacktabbedgap{1ex}
\tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1},
placed in a box 
\fbox{\,%
  \tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1}}\\
or saved%
\savestack\mybox{%
  \tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\2&3&1}}
for repeated use: \mybox, \fbox{\,\mybox}, \mybox.\\
Or with annotation:
\tabbedCenterstack[l]{0&1&2\\\updownarrow&\updownarrow&\updownarrow\\%
  2\bllap{\color{red}\tiny\mbox{This is important}\uparrow}&3%
  &\brlap{\color{red}\uparrow\tiny\mbox{but not this}}1
}
\end{document}

Answer 5

A PSTricks solution:

\documentclass{article}

\usepackage{multido,pstricks}

\def\Map(#1)#2#3{%
  \psline{<->}(#1,0)(#1,1)
  \rput(#1,-0.3){#2}
  \rput(#1,1.3){#3}}

% parameter
\def\arrows{3}

\begin{document}

\begin{pspicture}(0.95,-0.4)(\arrows.05,1.4) % boundry found manually
  \multido{\iA = 0+1, \iB = 1+1}{\arrows}{\Map(\iB){$\iA$}{$\iB$}}
\end{pspicture}

\end{document}

All you have to do is choose the value of \arrows and the drawing will be adjusted accordingly.

Answer 6

One more solution with tikz-cd:

% arara: pdflatex

\documentclass{article} 
\usepackage{tikz-cd}

\begin{document} 
\begin{tikzcd}[column sep=1.7em, every arrow/.append style={<->}]
    1\arrow{d} & 2\arrow{d} & 3\arrow{d} \\
    0 & 1 & 2
\end{tikzcd}
\end{document}

Answer 7

A MetaPost way of doing this:

prologues := 3;
outputtemplate := "%j-%c.mps";

input latexmp; setupLaTeXMP(options = "12pt", textextlabel = enable, mode = rerun);

% t[] values on top, b[] values on bottom
% u spacing between columns, v arrows length
vardef corresp(suffix t, b)(expr u, v) =
    save i; numeric i; i = 1;
    forever:
        exitif (unknown t[i]) or (unknown b[i]);
        drawdblarrow ((i-1)*u, 0) -- ((i-1)*u, v);
        label.top("$" & decimal t[i] & "$", ((i-1)*u, v)); 
        label.bot("$" & decimal b[i] & "$", ((i-1)*u, 0));
        i := i+1;
    endfor
enddef; 

% The OP's example
beginfig(1);
    numeric u, v, t[], b[]; u = 0.75cm; v = 0.75cm; 
    for i = 1 upto 3: b[i] = i-1; t[i] = i; endfor
    corresp(t, b)(u, v);
endfig;

% A bigger example
beginfig(2);
    numeric u, v, t[], b[]; u = cm; v = cm; 
    for i = 1 upto 7: t[i] = i-1; b[i] = (i-1)**2; endfor
    corresp(t, b)(u, v);
endfig;

end.

Horizontal spacing u between numbers can be adjusted at will, as for the arrows length v. As many numbers as wished at the top and the bottom can be entered, respectively in the arrays t[] and b[]. The corresp macro takes care of the subsequent job.

The code is supposed to be compiled by MetaPost with LaTeX as typesetting engine.

mpost --tex=latex program.mp

Two figures are produced by this code: The first one is the OP's example, the second one is another (bigger) example.