Discrete Polymatroids

TL;DR

This paper explores the combinatorial and algebraic properties of discrete polymatroids, extending the polyhedral theory of integral polymatroids to a multiset context.

Contribution

It introduces new combinatorial and algebraic insights into discrete polymatroids, building on classical polyhedral theory from the 1960s and 1970s.

Findings

Development of combinatorial properties of discrete polymatroids

Algebraic structures associated with discrete polymatroids

Extension of polyhedral theory to multiset analogues

Abstract

The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960's and in early 1970's, in the present paper the combinatorics and algebra on discrete polymatroids will be studied.