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\newcommand{\mb}[1]{\mathbb{#1}}
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\newcommand{\mf}[1]{\mathbf{#1}}
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\newcommand{\F}{\mb{F}}
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\newcommand{\G}{\mb{G}}
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\newcommand{\R}{\mb{R}}
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\newcommand{\Z}{\mb{Z}}
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\newcommand{\abs}[1]{\left| #1 \right|}
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\newcommand{\norm}[1]{\left\| #1 \right\|}
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\newcommand{\isomorphic}{\simeq}
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\newcommand{\To}{\rightarrow}
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\newcommand{\Emph}[1]{\emph{\textcolor{blue}{#1}}}
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\newcommand{\Cay}[1]{\operatorname{Cay}\left(#1\right)}
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\newcommand{\diag}[1]{\operatorname{diag}\left(#1\right)}
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\newcommand{\dual}[1]{\widetilde{#1}}
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\newcommand{\support}[1]{\operatorname{supp}\left(#1\right)}
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\newcommand{\weight}[1]{\operatorname{wt}\left(#1\right)}
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\newcommand{\weightclass}[1]{\operatorname{wc}\left(#1\right)}
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%
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\newenvironment{proofof}[1]{\noindent\emph{Proof of #1.}}{\qed}
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