Another approach to volume of matroid polytopes
Ahmed Umer Ashraf
TL;DR
This paper introduces a novel algorithm for calculating the volume of matroid base polytopes, with applications linking volumes of related matroids and deriving formulas for sparse paving matroids.
Contribution
It presents a new computational method for matroid polytope volumes and establishes relations and formulas specific to certain matroid classes.
Findings
Relation between volumes of matroid and relaxation matroids
Formula for volume of sparse paving matroid base polytopes
Algorithm improves volume computation for arbitrary matroids
Abstract
We present a new algorithm for computing the volume of an arbitrary matroid base polytope. We provide two applications of this approach: a relation between the volume of the base polytope of a matroid and its relaxation , and a formula for the volume of an arbitrary sparse paving matroid base polytope.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Computational Geometry and Mesh Generation · Data Management and Algorithms