In [BR01], [BR02], Bollobás and Riordan generalized the classical Tutte polynomial to graphs cellularly embedded in surfaces, i.e. ribbon graphs, thus encoding topological information not captured by the classical Tutte polynomial. We provide a ‘recipe theorem’ for their new topological Tutte polynomial, R(G). We then relate R(G) to the generalized transition polynomial Q(G) of [E-MS02] via a m...

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 ...