Stanley depth and simplicial spanning trees

Autor(en): Katthaen, Lukas
Stichwörter: DECOMPOSITIONS; LCM lattice; Mathematics; Monomial ideal; MULTIGRADED HILBERT DEPTH; Stanley conjecture; Stanley depth
Erscheinungsdatum: 2015
Herausgeber: SPRINGER
Journal: JOURNAL OF ALGEBRAIC COMBINATORICS
Volumen: 42
Ausgabe: 2
Startseite: 507
Seitenende: 536
Zusammenfassung: 
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.
ISSN: 09259899
DOI: 10.1007/s10801-015-0589-y

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