Computing the Stanley depth
نویسندگان
چکیده
منابع مشابه
Bounds of Stanley depth
We answer positively a question of Asia Rauf for the case of intersections of three prime ideals generated by disjoint sets of variables and we present several inequalities on Stanley depth. This is a detailed presentation of our talk at the conference on ”Fundamental structures of algebra” in honor of Prof. Serban Basarab at his 70-th anniversary. Let S = K[x1, . . . , xn] be a polynomial alge...
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We show that Stanley’s Conjecture holds for square free monomial ideals in five variables, that is the Stanley depth of a square free monomial ideal in five variables is greater or equal with its depth.
متن کاملStanley Depth of Multigraded Modules
The Stanley’s Conjecture on Cohen-Macaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, Soleyman-Jahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables.
متن کاملA Survey on Stanley Depth
At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals. (3) Ideals generated by two-minors with applications to Algebraic Statistics. In this artic...
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: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.11.025