English

Nullity Invariance for Pivot and the Interlace Polynomial

Discrete Mathematics 2014-03-26 v3 Combinatorics

Abstract

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.

Cite

@article{arxiv.0912.0878,
  title  = {Nullity Invariance for Pivot and the Interlace Polynomial},
  author = {Robert Brijder and Hendrik Jan Hoogeboom},
  journal= {arXiv preprint arXiv:0912.0878},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T14:19:42.247Z