Regularity comparison of symbolic powers, integral closure of powers and powers of edge ideals

Abstract

We study the regularity of small symbolic powers and integral closure of small powers of edge ideals. We also prove that the regularity of integral closure of powers of edge ideals of graphs with at most two odd cycles is the same as the regularity of their powers.

16 pages; Title has been changed, and results on the comparison of the regularity of small powers have been added. Comments and suggestions are welcome

References in corpus (3)

• A generalized Asymmetric Exclusion Process with $U_q({\mathfrak{sl}}_2)$ stochastic duality
• Stability of Associated Primes and Depth of Integral Closures of Powers of Edge Ideals
• Integral closure of small powers of edge ideals and their regularity

Cited by in corpus (3)

• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• A reverse duality for the ASEP with open boundaries
• Markov duality and Bethe ansatz formula for half-line open ASEP