English

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

Commutative Algebra 2013-12-16 v2 Combinatorics

Abstract

Let KK be a field and II a monomial ideal of the polynomial ring S=K[x1,...,xn]S=K[x_1,..., x_n] generated by monomials u1,u2,...,utu_1,u_2,..., u_t. We show that S/IS/I is pretty clean if either: 1) u1,u2,...,utu_1,u_2,..., u_t is a filter-regular sequence, 2) u1,u2,...,utu_1,u_2,..., u_t is a dd-sequence; or 3) II is almost complete intersection. In particular, in each of these cases, S/IS/I is sequentially Cohen-Macaulay and both Stanley's and hh-regularity conjectures, on Stanley decompositions, hold for S/IS/I. Also, we prove that if II is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on [n][n], then Stanley's conjecture holds for S/IS/I.

Keywords

Cite

@article{arxiv.1112.5159,
  title  = {Filter-regular sequences, almost complete intersections and Stanley's conjecture},
  author = {Somayeh Bandari and Kamran Divaani-Aazar and Ali Soleyman Jahan},
  journal= {arXiv preprint arXiv:1112.5159},
  year   = {2013}
}

Comments

This paper has been withdrawn by the authors. This paper was divided into the following two papers: "Pretty cleanness and filter-regular sequences" [arXiv:1312.0858] and "Almost complete intersections and Stanley's conjecture" [arXiv:1311.7303]

R2 v1 2026-06-21T19:55:29.093Z