English

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.

Keywords

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

R2 v1 2026-06-22T06:22:51.325Z