Multi-Path Matroids
Combinatorics
2024-08-07 v1
Abstract
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural properties. Key elements of this work are two complementary perspectives we develop for these matroids: on the one hand, multi-path matroids are transversal matroids that have special types of presentations; on the other hand, the bases of multi-path matroids can be viewed as sets of lattice paths in certain planar diagrams.
Cite
@article{arxiv.math/0410425,
title = {Multi-Path Matroids},
author = {Joseph E. Bonin and Omer Gimenez},
journal= {arXiv preprint arXiv:math/0410425},
year = {2024}
}
Comments
24 pages; 10 figures