K-theoretic Tutte polynomials of morphisms of matroids

Parametrized Tutte Polynomials of Graphs and Matroids

We generalize and unify results on parametrized and coloured Tutte polynomials of graphs and matroids due to Zaslavsky, and Bollobás and Riordan. We give a generalized Zaslavsky– Bollobás–Riordan theorem that characterizes parametrized contraction–deletion functions on minor-closed classes of matroids, as well as the modifications necessary to apply the discussion to classes of graphs. In gener...

Tutte Polynomials of Flower Graphs

Strongly Inequivalent Representations and Tutte Polynomials of Matroids

We develop constructive techniques to show that non-isomorphic 3-connected matroids that are representable over a fixed finite field and that have the same Tutte polynomial abound. In particular, for most prime powers q, we construct infinite families of sets of 3-connected matroids for which the matroids in a given set are non-isomorphic, are representable over GF(q), and have the same Tutte p...

Convolution-multiplication identities for Tutte polynomials of matroids

Abstract. We give a general multiplication-convolution identity for the multivariate and bivariate rank generating polynomial of a matroid. The bivariate rank generating polynomial is transformable to and from the Tutte polynomial by simple algebraic operations. Several identities, almost all already known in some form, are specialization of this identity. Combinatorial or probabilistic interpr...

Tutte Polynomials and Bicycle Dimension of Ternary Matroids

Let M be a ternary matroid, t(M,x,y) be its Tutte polynomial and d(M) be the dimension of the bicycle space of any representation of M over GF(3) . We show that, for j = e2'"/3, the modulus of the complex number t(M,j,j2) is equal to (v/3)'/(M) . The proof relies on the study of the weight enumerator Wv\y) of the cycle space £* of a representation of M over GF(3) evaluated at y = j . The main t...