Linear relations for a generalized Tutte polynomial (Q2341072)

Summary: \textit{T. Brylawski} [Trans. Am. Math. Soc. 171, 235--282 (1972; Zbl 0224.05007)] 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 \(\mathbb{R}^n\). It also gives a ``new'' linear relation for matroids that is implied by Brylawski's identities.