Filter-regular sequences, almost complete intersections and Stanley's conjecture

2011/12/21 by Bandari, Somayeh, Divaani-Aazar, Kamran, Jahan, Ali Soleyman
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.5159

Abstract

Let K be a field and I a monomial ideal of the polynomial ring S=K[x₁,..., x_n] generated by monomials u₁,u₂,..., u_t. We show that S/I is pretty clean if either: 1) u₁,u₂,..., u_t is a filter-regular sequence, 2) u₁,u₂,..., u_t is a d-sequence; or 3) I is almost complete intersection. In particular, in each of these cases, S/I is sequentially Cohen-Macaulay and both Stanley's and h-regularity conjectures, on Stanley decompositions, hold for S/I. Also, we prove that if I is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on [n], then Stanley's conjecture holds for S/I.

Related

• Almost complete intersections and Stanley's conjecture
• Pretty cleanness and filter-regular sequences
• A note on Stanley conjecture for monomial ideals
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• Sequentially Cohen-Macaulay and pretty clean monomial ideals