English

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

Combinatorics 2014-09-26 v2

Abstract

We show how the Tutte polynomial of a matroid MM 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 MM 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.

Keywords

Cite

@article{arxiv.1407.6666,
  title  = {Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats},
  author = {Jens Niklas Eberhardt},
  journal= {arXiv preprint arXiv:1407.6666},
  year   = {2014}
}

Comments

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