Text mode commands/symbols in math mode

Question

I am fairly new to LaTeX, and have run into a problem with commands apparently only available in text mode, where I would like to use them in math mode as well (e.g. integrated in equations).

One of the commands/symbols in question is the upside down exclamation sign used to represent the subfactorial function. In running text, I can use the command \textexclamdown, but this does not work in math mode (as far as I can tell).

Is there a way to seamlessly integrate text mode commands in the middle of rather hairy equations?

Answer 1

You can define your own symbol:

\documentclass{article}
\usepackage{amsmath}

\DeclareMathSymbol{\subfactorial}{\mathord}{operators}{"3C}

\begin{document}
\begin{equation}
\begin{aligned}
n!=\sum_k h(n,k) &= \sum_k \binom{n}{k}(n-k)\subfactorial\\
  &=\sum_k\binom{n}{k}k\subfactorial
\end{aligned}
\tag{5.49}
\end{equation}
\end{document}

This will work so long as the "operators" font is OT1 encoded. Should it be T1 encoded, change "3C" into "BD (this might depend on your font settings).

The equation (same number) is taken from "Discrete Mathematics", by Graham, Knuth and Patashnik (the original uses Euler fonts, but the result is quite similar).

Answer 2

Your question can be broken down into a few manageable parts.

1. Any text command can be used in mathmode if you use it as an argument to the \text macro, as in \text{\textexclamdown}.

2. To have it play the proper role in the spacing of the mathematics, you should embed this in a \mathord macro, as in \mathord{\text{\textexclamdown}}.

3. Because \mathord{\text{\textexclamdown}} is a bit cumbersome to write, and isn't very suggestive of what you want it to signify, I'd suggest writing a macro for the subfactorial function, similar to

   \newcommand\subfac{\mathord{\text{\textexclamdown}}}
   

   and then use \subfac to represent the subfactorial function. (This way if you decide that you would like to modify how the subfactorial is displayed, you can do it once and all instances of it will get changed.)