# How do I typeset the concatenation of strings properly?

I am looking for a good way to typeset the concatenation of two strings. This is standard notation in descriptive set theory to join an m-tuple x to an n-tuple y to get an (m+n)-tuple x^y, that is, a small slightly raised circumflex or frown joining the upper parts of the characters together. I currently use the straightforward

x^\smallfrown y


which doesn't look terribly good.

Semantically, this is a binary operation, but it shouldn't have the usual spacing on the right and the left and it should be higher up than a minus sign, say.

Here's a sample screen shot from Moschovakis's Descriptive set theory (p.76 of the pdf) which is approximately what I'd like to do, but I'd prefer a frown:

Looking around on this site, I found the question String/vector concatenation symbol but it is concerned with which symbol to use for the operation, so it doesn't address my question.

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Define a binary math command (\mathbin) that is typeset according to your specifications:

\documentclass{article}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\newcommand{\concatA}{%
\mathbin{\raisebox{1ex}{\scalebox{.7}{$\frown$}}}%
}
\newcommand{\concatB}{%
\mathbin{\rotatebox[origin=c]{90}{\scalebox{.7}{(\kern1ex)}}}
}
\begin{document}
$x\concatA y\ x\concatB y$
\end{document}​​​​​​​​​​​​​​​​​​​​​​​​​


\concatA could be what you're after, although I've also added \concatB to show you another possibility. There may be more, so if you're interested, see How to look up a symbol?.

You can fiddle around with the \frown raise (1ex) as well as the size (scaled to .7 of its original size thanks to graphicx).

It sounds logical to me to have the spacing set as \mathbin since it represents an operator acting on two entities (operands). However, you can use \mathord to remove the binary-operator-ness. Perhaps even specifying your own spacing around the symbol with additional \mkerns if needed.

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The original post asked to remove the spaces around the operator. So it would be better to use \mathord instead of \mathbin. –  Guido Sep 21 '12 at 0:02
Great! Thanks for the quick response (and the edit to my question). Yes, \concatA is essentially what I want, except for the spacing around the operation which is taken care of by @Guido's comment. I'll leave this open for a few hours to see if someone else has another suggestion but in my document it works the way I wanted. –  geezer Sep 21 '12 at 0:09
@Guido: True. I've referenced that in my answer. Thanks. –  Werner Sep 21 '12 at 0:14
There is one problem with the suggested solution: I often need the command in subscripts, e.g. N_{x \concatA y} and your solution doesn't seem to scale properly, like the ordinary operations like + do. How do I get it to do that? –  geezer Sep 21 '12 at 0:32
@geezer: That wasn't part of the original request. However, without repeating Guido's suggestion, see his answer for an alternative that provides this functionality. –  Werner Sep 21 '12 at 1:50

You can expand on Werner's solution using \mathchoice.

\newcommand{\concatA}{%
\mathord{
\mathchoice
{\raisebox{1ex}{\scalebox{.7}{$\frown$}}}
{\raisebox{1ex}{\scalebox{.7}{$\frown$}}}
{\raisebox{.7ex}{\scalebox{.5}{$\frown$}}}
{\raisebox{.7ex}{\scalebox{.5}{$\frown$}}}
}
}

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That led to exactly the solution I needed. Thanks a lot! –  geezer Sep 21 '12 at 1:56