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A generalization of weight polynomials to matroids

Permanent link
https://hdl.handle.net/10037/9077
DOI
https://doi.org/10.1016/j.disc.2015.10.005
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Accepted manuscript version (PDF)
Date
2015-11-11
Type
Tidsskriftartikkel
Journal article
Peer reviewed

Author
Johnsen, Trygve; Roksvold, Jan Nyquist; Verdure, Hugues
Abstract
Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M. Our main result is that these polynomials are determined by Betti numbers associated with N0-graded minimal free resolutions of the Stanley-Reisner ideals of M and so-called elongations of M. Generalizing Greene’s the- orem from coding theory, we show that the enumerator of a matroid is equivalent to its Tutte polynomial.
Description
Accepted manuscript version. Published version available at http://dx.doi.org/10.1016/j.disc.2015.10.005
Publisher
Elsevier
Citation
Discrete Mathematics 2016, 339(2):632-645
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