Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11942
Title: Nullity invariance for pivot and the interlace polynomial
Authors: BRIJDER, Robert 
Hoogeboom, Hendrik Jan
Issue Date: 2011
Publisher: ELSEVIER SCIENCE INC
Source: LINEAR ALGEBRA AND ITS APPLICATIONS, 435 (2). p. 277-288
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. (C) 2011 Elsevier Inc. All rights reserved.
Notes: [Brijder, Robert] Hasselt Univ, Diepenbeek, Belgium. [Brijder, Robert] Transnat Univ Limburg, Limburg, Belgium. [Hoogeboom, Hendrik Jan] Leiden Univ, Leiden Inst Adv Comp Sci, NL-2300 RA Leiden, Netherlands. robert.brijder@uhasselt.be
Keywords: Interlace polynomial; Principal pivot transform; Schur complement; Delta-matroid; Local complementation; Circle graph
Document URI: http://hdl.handle.net/1942/11942
ISSN: 0024-3795
e-ISSN: 1873-1856
DOI: 10.1016/j.laa.2011.01.024
ISI #: 000289335200007
Category: A1
Type: Journal Contribution
Validations: ecoom 2012
Appears in Collections:Research publications

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