Geodesic
Stanley depth and simplicial spanning trees
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 2, pp. 507-536.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 05E40, 05C05, 13D02, 55U10
Keywords: monomial ideal, LCM lattice, Stanley depth, Stanley conjecture 
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     title = {Stanley depth and simplicial spanning trees},
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Katthän, Lukas. Stanley depth and simplicial spanning trees. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 2, pp. 507-536. http://geodesic.mathdoc.fr/item/JAC_2015__42_2_a5/