amsmathmath-mode
How would one typeset basic combinatorics, like variation and combination?
For example, when using \(V'_n^k\) for variation with repetition, n and k are not vertically aligned. Something like \(V'\begin{smallmatrix}k\\n\end{smallmatrix}\) comes close, but the spacing is a little to wide, and it isn't left-aligned.
So, what's the best or usual way to do this? (Preferably also working with MathJax.)
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{gather*}
\mbox{\scriptsize%
$A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}$}\\
A = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}
\end{gather*}
\end{document}
[Note: the improvement below, actually does not work.]
[Note: there is an important improvement to this code below.]
The closest I can get to a solution is
\documentclass[10pt,a4paper]{article}
\usepackage{amsmath,amsthm,mathtools}
\begin{document}
\begin{proof}
\begin{align*}
15 &= 5+4+3+2+1 = \sum_{i=1}^5 i \\
120&=5\cdot4\cdot3\cdot2\cdot1 = 5! \\
\shortintertext{
\[ e^{\pi i} + 1 = 0 \]
\[ x^n + y^n = z^n \]
}
27 &= 3^3 \qedhere
\end{align*}
\end{proof}
\end{document}
which gives as result
and actually the spacing is quite nice, I think.
I think the below code is nicer, and even gives better results.
\documentclass[10pt,a4paper]{article}
\usepackage{amsmath,amsthm,mathtools}
\begin{document}
\begin{proof}
\begin{align*}
15 &= 5+4+3+2+1 = \sum_{i=1}^5 i \\
120&=5\cdot4\cdot3\cdot2\cdot1 = 5! \\
\begin{gathered}
e^{\pi i} + 1 = 0 \\
x^n + y^n = z^n
\end{gathered}
27 &= 3^3 \qedhere
\end{align*}
\end{proof}
\end{document}
Credits go to barbara beeton (please vote up her comment on her own answer).
Best Answer
I suggest the following code: