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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

8 votes
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802 views

Linear relations among permutation matrices

Given a permutation $\sigma\in S_n$, let $P_\sigma$ denote the corresponding $n\times n$ permutation matrix. It is easy to see that for $n=3$, there is only one linear relation up to scaling given by …