# Factorial spacing inside equation

Good day,

My minimum working example:

\documentclass[]{report}

\begin{document}

$$\hat{d}=\frac{(d+n)!}{n!d!}$$

\end{document}


The result is:

Now I don't like the spacing for the term: "n!d!". I'd prefer a bit more space between 'n' and '!' and between 'd' and '!'.

Any ideas?

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A short solution would be forcing a single space between them by using \ , like this: {n\ ! d\ !} –  Luan Resende Jun 24 '13 at 12:27
That would be incorrect. In case the ! is followed by an ordinary symbol, add a thin space: n!\,d!, but don't detach the ! from the symbol preceding it. –  egreg Jun 24 '13 at 12:32

It's incorrect to detach the ! meaning “factorial” from the symbol preceding it, because it's a modifier similar to a prime or a subscript and is not a punctuation symbol.

In case you have a factorial followed by an ordinary symbol (not a relation or operation symbol), it's good practice to add a thin space after it:

\documentclass{report}

\begin{document}

$\makebox[4em]{Good:} \hat{d}=\frac{(d+n)!}{n!\,d!}$
$\makebox[4em]{Bad:} \hat{d}=\frac{(d+n)\,!}{n\,!d\,!}$
\end{document}


I've also shown what would happen when detaching the factorial symbol, in order to demonstrate it would be wrong.

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I'm not familiar with TeX's ifttt syntax but wouldn't it be possible and useful to create a macro for this, say factorial, which checks automatically what follows after it and adds a thin space if appropriate? –  Pacific Orion Nov 24 '14 at 13:41
@PacificOrion The main problem is deciding when a space is appropriate and this is the main reason why it's declared as ordinary rather than punctuation. Having a space or not depends on several considerations. –  egreg Nov 24 '14 at 14:10
What would those be? Wouldn't adding a thin space whenever \factorial was followed by something other than } be a good start? –  Pacific Orion Nov 24 '14 at 14:37
@PacificOrion When \frac{n!}{2} is processed, ! won't be followed by } any more. –  egreg Nov 24 '14 at 14:43
Ah? I guess I don't know enough about TeX's parsing. Could \factorial check the user's input rather than the processed stuff? –  Pacific Orion Nov 24 '14 at 14:48