Linear relations for a generalized Tutte polynomial

Abstract

Brylawski proved the coefficients of the Tutte polynomial of a matroid satisfy a set of linear relations. We extend these relations to a generalization of the Tutte polynomial that includes greedoids and antimatroids. This leads to families of new identities for antimatroids, including trees, posets, chordal graphs and finite point sets in ℝn. It also gives a “new” linear relation for matroids that is implied by Brylawski's identities.