A generalization of weight polynomials to matroids
arXiv:1311.6291 · doi:10.1016/j.disc.2015.10.005
Abstract
Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid . Our main result is that these polynomials are determined by Betti numbers associated with graded minimal free resolutions of the Stanley-Reisner ideals of and so-called elongations of . Generalizing Greene's theorem from coding theory, we show that the enumerator of a matroid is equivalent to its Tutte polynomial.
21 pages