Abstract. We develop linear representation theory for bicircular matroids, a chief example being a matroid associated with forests of a graph, and bicircular lift matroids, a chief...
We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte...
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in Σp 2 . In the case of linear matroids, which are represented over poly...
Abstract. We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generaliz...