How do I stack more than two arrows in math mode?

Question

The command \rightrightarrows (from amssymb) draws two arrows, one on top of another. How do I get three arrows arranged in a similar fashion? An example of this (and other fancy arrow stackings) appears on page 3 of this paper, for which a source file unfortunately does not seem to be available. Commands like \stackrel and \overset do not size or space things properly.

Answer 1

Use TikZ!

\documentclass{article}

\usepackage{tikz}

\newcommand{\triplerightarrow}{%
\tikz[minimum height=0ex]
  \path[->]
   node (a)            {}
   node (b) at (1em,0) {}
  (a.north)  edge (b.north)
  (a.center) edge (b.center)
  (a.south)  edge (b.south);%
}

\begin{document}

\[
A \triplerightarrow B
\]
\end{document}

The minimum height=0ex doesn't do anything. I included it to show how to increase the separation of the arrows if desired. To get longer arrows, increase the 1em (this could be made an optional parameter, of course, and with a bit of work could be made so that there was a(nother) parameter specifying some text on top whereupon the arrows scaled to the correct length).

Answer 2

How about the following?

\newcommand\rightthreearrow{%
        \mathrel{\vcenter{\mathsurround0pt
                \ialign{##\crcr
                        \noalign{\nointerlineskip}$\rightarrow$\crcr
                        \noalign{\nointerlineskip}$\rightarrow$\crcr
                        \noalign{\nointerlineskip}$\rightarrow$\crcr
                }%
        }}%
}

This is basically how \overbrace works except that it uses a fill and a \vbox instead of a \vcenter.

Answer 3

You can mess around with XY-pic, the \xymatrix command in particular could be used. You might begin with the XY-pic User's Guide (pdf).

For example, if you \input xy and \xyoption{all} in your preamble, then

 \[\xymatrix{
  A\ar@<1ex>[r]\ar[r]\ar@<-1ex>[r] & B
 }\]

Will produce 3 arrows from A to B.

Answer 4

Inspired by \threesim in symbols-a4, which stacks three \sim symbols, here's a solution for stacking and vertically centering a symbol three times:

\newcommand*{\triple}[2][.1ex]{%
  \mathrel{\vcenter{\offinterlineskip%
  \hbox{$#2$}\vskip#1\hbox{$#2$}\vskip#1\hbox{$#2$}}}}

You may use it to stack three right or left arrows or others, just a dot for example:

\newcommand*{\triplerightarrow}{\triple{\rightarrow}}
\newcommand*{\tripleleftarrow}{\triple{\leftarrow}}
\newcommand*{\tripledot}{\triple[-.6ex]{\cdot}}

Example:

$X\triplerightarrow Y\tripledot\tripleleftarrow Z$

You might adjust the spacing using the optional argument, perhaps choose another arrow with a smaller tip if you like.

Answer 5

Use \substack

$X\substack{\rightarrow\\[-1em] \rightarrow \\[-1em] \rightarrow} Y$

you can change [-1em] to be any value as you want.

(Added by Hendrik Vogt:) With

$X \mathrel{\substack{\textstyle\rightarrow\\[-0.6ex]
                      \textstyle\rightarrow \\[-0.6ex]
                      \textstyle\rightarrow}} Y$

you get something quite close to \rightrightarrows.