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arXiv · 2111.14175

Regularity of powers of (parity) binomial edge ideals

Yi-Huang Shen·Guangjun Zhu
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Abstract

In this paper, we provide exact formulas for the Castelnuovo-Mumford regularity of powers of an almost complete intersection ideal $I$ which is generated by a homogeneous $d$-sequence. As applications, when $I$ is an almost complete intersection, taking the form of the (parity) binomial edge ideal of a connected graph, we can describe explicitly formulas for $\reg(I^t)$ for $t\ge 2$. The only exception is when $I$ is the parity binomial edge ideal of a graph which is obtained by adding an edge between two disjoint odd cycles.

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Yi-Huang Shen, Guangjun Zhu. 2021-11-28. Regularity of powers of (parity) binomial edge ideals. https://arxiv.org/abs/2111.14175

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