Nullity Invariance for Pivot and the Interlace Polynomial

Details Nullity Invariance for Pivot and the Interlace Polynomial Nullity Invariance for Pivot and the Interlace Polynomial

2009-12-04

arxiv.org/abs/0912.0878v3

Computer Science

Discrete Mathematics

small revision of Section 8 w.r.t. v2, 14 pages, 6 figures

Scientific paper

We show that the effect of principal pivot transform on the nullity values of
the principal submatrices of a given (square) matrix is described by the
symmetric difference operator (for sets). We consider its consequences for
graphs, and in particular generalize the recursive relation of the interlace
polynomial and simplify its proof.

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