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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/15199

Title: NULLITY AND LOOP COMPLEMENTATION FOR DELTA-MATROIDS
Authors: Brijder, Robert
Hoogeboom, Hendrik Jan
Issue Date: 2013
Publisher: SIAM PUBLICATIONS
Citation: SIAM JOURNAL ON DISCRETE MATHEMATICS, 27 (1), p. 492-506
Abstract: We show that the symmetric-difference distance measure for set systems, and more specifically for delta-matroids, corresponds to the notion of nullity for symmetric and skew-symmetric matrices. In particular, as graphs (i.e., symmetric matrices over GF(2)) may be seen as a special class of delta-matroids, this distance measure generalizes the notion of nullity in this case. We characterize delta-matroids in terms of equicardinality of minimal sets with respect to inclusion (in addition, we obtain similar characterizations for matroids). In this way, we find that, e.g., the delta-matroids obtained after loop complementation and after pivot on a single element together with the original delta-matroid fulfill the property that two of them have equal "null space" while the third has a larger dimension.
Notes: Hasselt Univ, Hasselt, Belgium. Transnat Univ Limburg, Diepenbeek, Belgium. Leiden Univ, Leiden Inst Adv Comp Sci, Leiden, Netherlands.
URI: http://hdl.handle.net/1942/15199
Link to publication: http://arxiv.org/abs/1010.4497
DOI: 10.1137/110854692
ISI #: 000316868600030
ISSN: 0895-4801
Category: A1
Type: Journal Contribution
Validation: ecoom, 2014
Appears in Collections: Research publications

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