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Fast Odd-Permutation Sums in Characteristic Two and Shortest Even Directed Cycles
For a matrix $A$ over a field of characteristic two, let $Φ(A)$ be the sum of its permutation monomials indexed by odd permutations. Although determinant and permanent coincide in this characteristic, this parity sub-sum retains information that neither gives separately. We show that $Φ(A)$ and all
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