منابع مشابه
Stanley Decompositions and Polarization
We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal I is a CM Stanley ideal, then I is a Stanley ideal as well, where I is the polarization of I .
متن کاملStanley Decompositions and Partionable Simplicial Complexes
We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.
متن کاملStanley Decompositions and Partitionable Simplicial Complexes
We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.
متن کاملStanley Decompositions of Squarefree Modules and Alexander Duality
In this paper we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial ring and the exterior algebra behave with respect to Alexander duality.
متن کاملThe behavior of Stanley depth under polarization
Let K be a field, R = K[X1, . . . ,Xn] be the polynomial ring and J ( I two monomial ideals in R. In this paper we show that sdepth I/J− depth I/J = sdepth I /J p − depth I /J , where sdepth I/J denotes the Stanley depth and I p denotes the polarization. This solves a conjecture by Herzog [Her13] and reduces the famous Stanley conjecture (for modules of the form I/J) to the squarefree case. As ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2011
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-011-0067-1