Multi-Path Matroids

Details Multi-Path Matroids Multi-Path Matroids

2004-10-19

arxiv.org/abs/math/0410425v1

Mathematics

Combinatorics

24 pages; 10 figures

Scientific paper

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.

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