Bounded powers of edge ideals: symmetric exchange binomials

TL;DR

This paper investigates the generation of toric ideals of discrete polymatroids, especially those derived from bounded powers of edge ideals of graphs, confirming the symmetric exchange binomials conjecture in specific cases.

Contribution

It provides new classes of discrete polymatroids with toric ideals generated by symmetric exchange binomials, focusing on bounded powers of edge ideals.

Findings

Identifies classes of discrete polymatroids with symmetric exchange binomial generators

Confirms the conjecture for polymatroids from bounded powers of edge ideals

Enhances understanding of the algebraic structure of graph-based polymatroids

Abstract

It has been conjectured that the toric ideal of the base ring of a discrete polymatroid is generated by symmetric exchange binomials. In the present paper, we give several classes of discrete polymatroids which yield toric ideals generated by symmetric exchange binomials. Especially, we are interested in the discrete polymatroids arising from bounded powers of edge ideals of finite graphs.