Stanley depth and simplicial spanning trees
Commutative Algebra
2015-03-10 v2 Combinatorics
Abstract
We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection with the simplicial spanning trees of skeletons of a simplex. We apply this result to verify the Stanley conjecture for quotients of monomial ideals with up to six generators. For seven generators we obtain a partial result.
Cite
@article{arxiv.1410.3666,
title = {Stanley depth and simplicial spanning trees},
author = {Lukas Katthän},
journal= {arXiv preprint arXiv:1410.3666},
year = {2015}
}
Comments
29 pages; some proofs clarified and many small corrections. To appear in J. Alg. Comb