Draw a box around selected entries of array
With a simple array
environment:
\documentclass[12pt]{article}
\usepackage{array,amsmath}
\begin{document}
$\arraycolsep=2pt
\begin{array}{ | *7c | *8c }\cline{1-7}
\rule{0pt}{3ex}% more vertical space for 1st line
c^{(1)} & \geq & c^{(2)} & \geq & \cdots & \geq & c^{(j)} & \geq & \cdots & \geq &
c^{((N-1)K+1)} & \geq & \cdots & \geq & c^{(NK)}\\
\downarrow & & \downarrow & & & & \downarrow & & & & \downarrow & & & &
\downarrow \\
\gamma^{(1)} & & \gamma^{(2)} & & \cdots & & \gamma^{(j)} & & \cdots & &
\gamma^{((N-1)K+1)}& &\cdots & & \gamma^{(NK)}\\\cline{1-7}
\end{array}
$
\end{document}
Using tcolorbox package
\documentclass[10.0pt,a4paper]{article}
\usepackage[all]{tcolorbox}
\usepackage[english]{babel}
\begin{document}
\begin{minipage}{5mm}
\begin{tcolorbox}[enhanced,arc=0mm,boxrule=1.5mm,frame hidden,colback=green!8!white,borderline={1mm}{0mm}{black,dotted},text width=5cm]
$\begin{array}{ccccccc}
c^{(1)} & \geq & c^{(2)} & \geq & \cdots & \geq & c^{(j)}\\ %& \geq & \cdots & \geq & c^{((N-1)K+1)} & \geq & \cdots & \geq & c^{(NK)}\\
\downarrow & & \downarrow & & & & \downarrow \\ %\downarrow & & & & \downarrow & & & & \downarrow &\\
\gamma^{(1)} & & \gamma^{(2)} & & \cdots & & \gamma^{(j)}\\ %& & \cdots & & \gamma^{((N-1)K+1)}& &\cdots & & \gamma^{(NK)}
\end{array}$
\end{tcolorbox}
\end{minipage}\hfill\hfill\hfill
\raisebox{0.5ex}{\begin{minipage}{5mm}
$\begin{array}{ccccccccc}
\geq & \cdots & \geq & c^{((N-1)K+1)} & \geq & \cdots & \geq & c^{(NK)}\\
& & & \downarrow & & & & \downarrow \\
& \cdots & & \gamma^{((N-1)K+1)}& &\cdots & & \gamma^{(NK)}
\end{array}$
\end{minipage}}\hfill\hfill~
\end{document}
Using TikZ Matrix nodes
\documentclass[10pt,a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{center}
\begin{tikzpicture}
\matrix [column sep=1mm]
{
\node (a) {};& & & & & & & & \node (b) {}; & & & & & & & \\
&\node {$c^{(1)}$}; & \node {$\geq$}; & \node {$c^{(2)}$}; & \node {$\geq$}; & \node {$\cdots$}; & \node {$\geq$}; & \node {$c^{(j)}$}; & &\node {}; \node {$\geq$}; & \node {$\cdots$}; & \node {$\geq$}; & \node {$c^{((N-1)K+1)}$}; & \node {$\geq$}; & \node {$\cdots$}; & \node {$\geq$}; & \node {$c^{(NK)}$};\\
&\node {$\downarrow$}; & & \node {$\downarrow$}; & & & & \node {$\downarrow$}; & & & & & \node {$\downarrow$}; & & & & \node {$\downarrow$}; \\
&\node {$\gamma^{(1)}$}; & & \node {$\gamma^{(2)}$}; & & \node {$\cdots$}; & & \node {$\gamma^{(j)}$}; &\node {};& & \node {$\cdots$}; & & \node {$\gamma^{((N-1)K+1)}$}; & & \node {$\cdots$}; & & \node {$\gamma^{(NK)}$};\\
\node (c) {};& & & & & & & & \node (d) {}; & & & & & & & \\
};
\draw [black,thick,dashed] (a.east) -- (c.east) {};
\draw [black,thick,dashed] (d.west) -- (b.west) {};
\draw [black,thick,dashed] (a.east) -- (b.west) {};
\draw [black,thick,dashed] (c.east) -- (d.west) {};
\end{tikzpicture}
\end{center}
\end{document}
With a tikz matrix
:
\documentclass[12pt]{article}
\usepackage{array,amsmath}
\usepackage{tikz}
\usetikzlibrary{matrix,fit}
\begin{document}
\begin{center}
\begin{tikzpicture}
\matrix[matrix of math nodes](m){%
c^{(1)} & \geq & c^{(2)} & \geq & \cdots & \geq & c^{(j)} &[8pt] \geq & \cdots & \geq & c^{((N-1)K+1)} & \geq & \cdots & \geq & c^{(NK)}\\
\downarrow & & \downarrow & & & & \downarrow & & & & \downarrow & & & & \downarrow \\
\gamma^{(1)} & & \gamma^{(2)} & & \cdots & & \gamma^{(j)} & & \cdots & & \gamma^{((N-1)K+1)}& &\cdots & & \gamma^{(NK)}\\
};
\node[fit=(m-1-1)(m-3-7), draw, thick] {};
\end{tikzpicture}
\end{center}
\end{document}