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How to display a smile symbol like this? For example, the k_2th place is a_1. enter image description here

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Use \overset and \substack:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\place}[2]{%
  \overset{\substack{#1\\\smile}}{#2}%
}

\begin{document}
\[
(\place{1}{a_{1}},a_{2},\dots,\place{k_{2}}{a_{1}},
 a_{2},\dots,\place{k_{3}}{a_{2}},
 a_{3},\dots,\place{k_{r+1}}{a_{r}},
 b_{m+1},\dots,b_{n})
\]
\end{document}

enter image description here

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