The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.1991 Mathematics Subject Classification. 13C13, 13A30, 13F99, 05E40.
Let L be a distributive lattice and R(L) the associated Hibi ring. We compute reg R(L) when L is a planar lattice and give bounds for reg R(L) when L is non-planar, in terms of the combinatorial data of L. As a consequence, we characterize the distributive lattices L for which the associated Hibi ring has a linear resolution.1991 Mathematics Subject Classification. 05E40,13D02,16E05.
Abstract. We introduce the concept of Stanley decompositions in the localized polynomial ring S f where f is a product of variables, and we show that the Stanley depth does not decrease upon localization. Furthermore it is shown that for monomial ideals J ⊂ I ⊂ S f the number of Stanley spaces in a Stanley decomposition of I/J is an invariant of I/J. For the proof of this result we introduce Hilbert series for Z n -graded K-vector spaces.
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