Stanley depth and simplicial spanning trees. (English) Zbl 1319.05157
Summary: 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.
MSC:
| 05E40 | Combinatorial aspects of commutative algebra |
| 05C05 | Trees |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
| 55U10 | Simplicial sets and complexes in algebraic topology |
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