Latex Math Symbol

The symbol is available in Unicode: U+29E2 Shuffle product

LuaTeX/XeTeX

• Asana Math:

  \documentclass{article}  
  \usepackage{unicode-math}   
  \setmathfont{Asana-Math.otf}
  \begin{document}
  \[A \shuffle B\]
  \end{document}
  

  

• XITS Math

  \setmathfont{xits-math.otf}
  

  

• Not available in

  • Latin Modern Math
  • TeX Gyre Math fonts

Metafont

• Package shuffle:

  \documentclass{article}
  \usepackage{shuffle}
  \begin{document}
  \[A \shuffle B\]
  \end{document}
  

  

  Or with support of any sizes (especially < 5pt, see Shuffle symbol breaks footnotes?):

  \documentclass{article}
  
  \DeclareSymbolFont{Shuffle}{U}{shuffle}{m}{n}
  \DeclareFontFamily{U}{shuffle}{}
  \DeclareFontShape{U}{shuffle}{m}{n}{%
    <-8>shuffle7%
    <8->shuffle10%
  }{}
  \DeclareMathSymbol\shuffle{\mathbin}{Shuffle}{"001}
  \DeclareMathSymbol\cshuffle{\mathbin}{Shuffle}{"002}
  
  \begin{document}
  \[ A \shuffle B \]
  \end{document}
  

Symbol composition with rules

Packages are not needed.

\documentclass{article}

\makeatletter
\providecommand*{\shuffle}{%
  \mathbin{\mathpalette\shuffle@{}}%
}
\newcommand*{\shuffle@}[2]{%
  % #1: math style
  % #2: unused
  \sbox0{$#1\vcenter{}$}%
  \kern .15\ht0 % side bearing
  \rlap{\vrule height .25\ht0 depth 0pt width 2.5\ht0}%
  \raise.1\ht0\hbox to 2.5\ht0{%
    \vrule height 1.75\ht0 depth -.1\ht0 width .17\ht0 %
    \hfill
    \vrule height 1.75\ht0 depth -.1\ht0 width .17\ht0 %
    \hfill
    \vrule height 1.75\ht0 depth -.1\ht0 width .17\ht0 %
  }%
  \kern .15\ht0 % side bearing
}
\makeatother

\begin{document}
\[
  A \shuffle B_{A \shuffle B_{A \shuffle B}}
\]
\end{document}

This combines two \sqcups and uses \mathchoice so that it sets in any mathstyle.

\documentclass{article}
\def\dsqcup{\sqcup\mathchoice{\mkern-7mu}{\mkern-7mu}{\mkern-3.2mu}{\mkern-3.8mu}\sqcup}
\begin{document}
$A \dsqcup B$

$\scriptstyle A \dsqcup B$

$\scriptscriptstyle A \dsqcup B$
\end{document}

\shuffle is defined in the stix package.