How to make a diagram like this in LaTeX?

Question

Does anybody know how to make this type of diagram in LaTeX with arrows and notations? (Example diagram is from Wikipedia).

Answer 1

With tikz-cd:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}
% based on \binom
\newcommand{\stirlingi}[2]{\genfrac[]{0pt}{}{#1}{#2}}
\newcommand{\stirlingii}[2]{\genfrac{}{0pt}{}{#1}{#2}}
\newcommand{\tstirlingi}[2]{\genfrac[]{0pt}{1}{#1}{#2}}
\newcommand{\tstirlingii}[2]{\genfrac{}{0pt}{1}{#1}{#2}}
\begin{document}
[
\begin{tikzcd}[row sep=8em,column sep=4em]
& x^n \arrow[dl,bend right=20,"(-1)^{n-k}\tstirlingii{n}{k}"']
      \arrow[dr,"\tstirlingii{n}{k}"']
\
x^{(n)} \arrow[ur,"\tstirlingi{n}{k}"']
        \arrow[rr,"{L(n,k)}"]
&&
(x)_{n} \arrow[ul,bend right=20,"(-1)^{n-k}\tstirlingi{n}{k}"']
        \arrow[ll,bend left=15,"{(-1)^{n-k}L(n,k)}"]
\end{tikzcd}
]
\end{document}

I'd avoid large labels like in the picture you show.

The braces in the labels with L(n,k) are necessary in order to avoid TikZ mistaking the comma for something that separates options.

Answer 2

With xy:

\documentclass[border=10pt]{standalone}
\usepackage{amsmath,amssymb}
\usepackage[all]{xy}
\begin{document}
$$
\xymatrix@C+2.5em@R+2.5em{
    &
    x^n
        \ar[ddr]*{\begin{Bmatrix}n\k\end{Bmatrix}}
        \ar@/_15pt/[ddl]{(-1)^{n-k}\begin{Bmatrix}n\k\end{Bmatrix}}

    & \
    &  & \
    x^{(n)}
        \ar[rr]^{L(n,k)}
        \ar[uur]*{\begin{bmatrix}n\k\end{bmatrix}}
    & &
    (x){n}
        \ar@/^15pt/[ll]^{(-1)^{n-k}L(n,k)}
        \ar@/15pt/[uul]{(-1)^{n-k}\begin{bmatrix}n\k\end{bmatrix}}
}
$$
\end{document}