Filter-regular sequences, almost complete intersections and Stanley's conjecture
Abstract
Let be a field and a monomial ideal of the polynomial ring generated by monomials . We show that is pretty clean if either: 1) is a filter-regular sequence, 2) is a -sequence; or 3) is almost complete intersection. In particular, in each of these cases, is sequentially Cohen-Macaulay and both Stanley's and -regularity conjectures, on Stanley decompositions, hold for . Also, we prove that if is the Stanley-Reisner ideal of a locally complete intersection simplicial complex on , then Stanley's conjecture holds for .
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This paper has been withdrawn by the authors.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]