Betti table Stabilization of Homogeneous Monomial Ideals

Abstract

Given an homogeneous monomial ideal I, we provide a question-and examplebased investigation of the stabilization patterns of the Betti tables shapes of I d as we vary d. We build off Whieldon's definition of the stabilization index of I, Stab(I), to define the stabilization sequence of I, StabSeq(I), and use it to explore changes in the shapes of the Betti tables of I d as we vary d. We also present the stabilization indices and sequences of the collection of ideals {In} where In = (a 2n b 2n c 2n , b 4n c 2n , a 3n c 3n , a 6n−1 b) ⊆ k[a, b, c].