Pseudodeterminants and perfect square spanning tree counts

Abstract

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or skewsymmetric matrix then pdet(∂∂t) = pdet(∂)2. Whenever ∂ is the kth boundary map of a self-dual CWcomplex X, this linear-algebraic identity implies that the… (More)
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