October 15, 2025Open Access

Bounded powers of edge ideals: symmetric exchange binomials

Key Points

Toric ideals can be generated by symmetric exchange binomials in discrete polymatroids, highlighting their structural properties.
Classes of discrete polymatroids identified yield toric ideals particularly important for theoretical developments.
The focus on bounded powers of edge ideals of finite graphs suggests new avenues for exploration in combinatorial optimization.
Results indicate deeper connections within graph theory and algebra, positioning symmetric exchange binomials as significant contributors.

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.

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Cite This Study

Hibi et al. (Wed,) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba063553b4 https://doi.org/https://doi.org/10.48550/arxiv.2507.11815

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