1 99 7 a Convolution Formula for the Tutte Polynomial

Let M be a finite matroid with rank function r. We will write A ⊆ M when we mean that A is a subset of the ground set of M , and write M | A and M/A for the matroids obtained by restricting M to A, and contracting M on A respectively. Let M * denote the dual matroid to M. (See [1] for definitions). The main theorem is Theorem 1. The Tutte polynomial T M (x, y) satisfies (1) T M (x, y) = A⊆M T M|A (0, y)T M/A (x, 0). First we define a convolution product and note a useful lemma. Let M be the set of all isomorphism classes of finite matroids, and let K be a commutative ring with 1.