English

The Merino--Welsh conjecture for split matroids

Combinatorics 2023-09-11 v2

Abstract

In 1999 Merino and Welsh conjectured that evaluations of the Tutte polynomial of a graph satisfy an inequality. In this short article we show that the conjecture generalized to matroids holds for the large class of all split matroids by exploiting the structure of their lattice of cyclic flats. This class of matroids strictly contains all paving and copaving matroids.

Keywords

Cite

@article{arxiv.2204.07132,
  title  = {The Merino--Welsh conjecture for split matroids},
  author = {Luis Ferroni and Benjamin Schröter},
  journal= {arXiv preprint arXiv:2204.07132},
  year   = {2023}
}

Comments

9 pages, 1 figure. Final version, accepted in Annals of Combinatorics

R2 v1 2026-06-24T10:48:30.337Z