A generalization of weight polynomials to matroids
ForfatterJohnsen, Trygve; Roksvold, Jan Nyquist; Verdure, Hugues
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.
Accepted manuscript version. Published version available at http://dx.doi.org/10.1016/j.disc.2015.10.005