Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats

Abstract

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 polynomial of $M$ is already determined by the abstract lattice of its cyclic flats together with their cardinalities and ranks. They furthermore generalize a similiar statement for perfect matroid designs due to Mphako and help to understand families of matroids with identical Tutte polynomial as constructed by Ken Shoda.

New version published in: Electronic Journal Of Combinatorics Volume 21, Issue 3 (2014) http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p47