The complexity of the $q$ -analog of the $n$ -cube

preprint2011arXivOpen access

We present a positive, combinatorial, good formula for the complexity (= number of spanning trees) of the $q$ -analog of the $n$ -cube. Our method also yields the explicit block diagonalization of the commutant of the $GL(n,F_q)$ action on the $q$ -analog of the Boolean algebra.

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The complexity of the $q$ -analog of the $n$ -cube

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The complexity of the qqq-analog of the nnn-cube

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The complexity of the $q$ -analog of the $n$ -cube