Splittings for symbolic powers of edge ideals of complete graphs

2023/09/22 by Cooper, Susan M., Da Silva, Sergio, Gutkin, Max +1 · 1 citation
#13D02 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.13017

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.

Cited by

• Symbolic Powers of Toric Ideals

Related

• Splittings of monomial ideals
• Upper bounds for the regularity of symbolic powers of certain classes of edge ideals
• Regularity of Symbolic Powers of Edge Ideals
• Invariants of the symbolic powers of edge ideals
• Symbolic Powers and Symbolic Rees Algebras of Binomial Edge Ideals of Some Classes of Block Graphs