3 papers
math.AC2024
A New Conjecture and Upper Bound on the Castelnuovo--Mumford Regularity of Binomial Edge Ideals
Adam LaClair
A famous theorem of Kalai and Meshulam is that for any squarefree monomial ideals and . This result was subse…
math.AC2023
Combinatorics of Castelnuovo-Mumford Regularity of Binomial Edge Ideals
Adam LaClair
Since the introduction of binomial edge ideals by Herzog et al. and independently Ohtani, there has been significant interest in relating algebraic invariants of the binomi…
math.AC2023
Invariants of Binomial Edge Ideals via Linear Programs
Adam LaClair
We associate to every graph a linear program for packings of vertex disjoint paths. We show that the optimal primal and dual values of the corresponding integer program are the bin…