$M$-Shellability of Discrete Polymatroids

TL;DR

This paper proves that all discrete polymatroids are $M$-shellable, confirming a conjecture in a special case and enhancing understanding of the combinatorial properties of these structures.

Contribution

It establishes that every discrete polymatroid is $M$-shellable, advancing the theory of polymatroid shellability and related combinatorial conjectures.

Findings

All discrete polymatroids are $M$-shellable.

Provides a partial positive answer to Chari's conjecture.

Improves results related to Stanley's conjecture for lattice path matroids.

Abstract

In this note we show that every discrete polymatroid is $M$-shellable. This gives, in a partial case, a positive answer to a conjecture of Chari and improves a recent result of Schweig where he proved that the $h$-vector of a lattice path matroid satisfies a conjecture of Stanley.