The Tutte polynomial of a graph or a matroid, named after WT Tutte, has the important
universal property that essentially any multiplicative graph or network invariant with a …

Enumerative combinatorics is about counting. The typical question is to find the number of
objects with a given set of properties. However, enumerative combinatorics is not just about …

This chapter treats error-correcting codes and their weight enumerator as the center of
several closely related topics such as arrangements of hyperplanes, graph theory, matroids …

We study the generalized and extended weight enumerator of the q-ary Simplex code and
the q-ary first order Reed-Muller code. For our calculations we use that these codes …

We show how the Tutte polynomial of a matroid $ M $ can be computed from its condensed
configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte …

Abstract In 1977, Yu. V. Matiyasevich proposed a formula expressing the chromatic
polynomial of an arbitrary graph as a linear combination of flow polynomials of subgraphs of …

On the Complexity of Computing the Tutte Polynomial of Bicircular Matroids Page 1
Combinatorics, Probability and Computing (2006) 15, 385–395. c 2006 Cambridge University …

We give a general convolution–multiplication identity for the multivariate and bivariate rank
generating polynomial of a graph or matroid. The bivariate rank generating polynomial is …

Cycle index, weight enumerator, and Tutte polynomial Page 1 Cycle index, weight enumerator,
and Tutte polynomial Peter J. Cameron School of Mathematical Sciences Queen Mary …

In this paper, we consider the coboundary polynomial for a matroid as a generalization of
the weight enumerator of a linear code. By describing properties of this polynomial and of a …