Splittings for symbolic powers of edge ideals of complete graphs
Susan M. Cooper, Sergio Da Silva, Max Gutkin, and Tessa Reimer
TL;DR
This paper investigates the symbolic powers of edge ideals in complete graphs, providing criteria for their algebraic splittings and detailed descriptions of their graded Betti numbers, extending to parallelizations of graphs.
Contribution
It introduces a criterion for Eliahou-Kervaire splitting of symbolic powers of edge ideals in complete graphs and describes their graded Betti numbers, also exploring parallelizations.
Findings
Established a criterion for Eliahou-Kervaire splitting of symbolic powers.
Provided explicit descriptions of graded Betti numbers for these ideals.
Extended analysis to edge ideals of graph parallelizations.
Abstract
In this paper we study the -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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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Polynomial and algebraic computation