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arXiv · 2405.07365

Multidegrees of binomial edge ideals

Jacob Cooper·Ethan Leventhal
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Abstract

Let $G$ be a simple graph with binomial edge ideal $J_G$. We prove how to calculate the multidegree of $J_G$ based on combinatorial properties of $G$. In particular, we study the set $S_{\min}(G)$ defined as the collection of subsets of vertices whose prime ideals have minimum codimension. We provide results which assist in determining $S_{\min}(G)$, then calculate $S_{\min}(G)$ for star, horned complete, barbell, cycle, wheel, and friendship graphs, and use the main result of the paper to obtain the multidegrees of their binomial edge ideals.

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Jacob Cooper, Ethan Leventhal. 2024-05-12. Multidegrees of binomial edge ideals. https://arxiv.org/abs/2405.07365

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