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arXiv · 2309.13017

Splittings for symbolic powers of edge ideals of complete graphs

Susan M. Cooper·Sergio Da Silva·Max Gutkin·Tessa Reimer
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Abstract

In this paper we study the $s$-th symbolic powers of the edge ideals of complete graphs. In particular, we provide a criterion for finding an Eliahou-Kervaire splitting on these ideals, and use the splitting to provide a description for the graded Betti numbers. We also discuss the symbolic powers and graded Betti numbers of edge ideals of parallelizations of finite simple graphs.

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Susan M. Cooper, Sergio Da Silva, Max Gutkin, Tessa Reimer. 2023-09-22. Splittings for symbolic powers of edge ideals of complete graphs. https://arxiv.org/abs/2309.13017

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