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135
Computing the Stanley depth
- J. Algebra
"... Abstract. Let Q and Q ′ be two monomial primary ideals of a polynomial algebra S over a field. We give an upper bound for the Stanley depth of S/(Q ∩Q ′ ) which is reached if Q,Q ′ are irreducible. Also we show that Stanley’s Conjecture holds for Q1 ∩ Q2, S/(Q1 ∩ Q2 ∩ Q3), (Qi)i being some irreducib ..."
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Cited by 11 (5 self)
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Abstract. Let Q and Q ′ be two monomial primary ideals of a polynomial algebra S over a field. We give an upper bound for the Stanley depth of S/(Q ∩Q ′ ) which is reached if Q,Q ′ are irreducible. Also we show that Stanley’s Conjecture holds for Q1 ∩ Q2, S/(Q1 ∩ Q2 ∩ Q3), (Qi)i being some
STANLEY CONJECTURE IN SMALL EMBEDDING DIMENSION
, 2007
"... Abstract. We show that Stanley’s conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals. ..."
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Cited by 26 (4 self)
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Abstract. We show that Stanley’s conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.
WHAT IS... STANLEY DEPTH?
"... Richard P. Stanley is well known for his fundamental and important contributions to combinatorics and its relationship to algebra and geometry, in particular in the theory of simplicial complexes. Two kinds of simplicial complexes play central roles in combinatorics: partitionable complexes and Cohe ..."
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is to introduce the notion of the Stanley depth. Let K be a field and S = K[x1,..., xn] the K-algebra of polynomials over K in n indeterminates x1,..., xn. We may write x = {x1,..., xn} and denote S by K[x] for convenience. A monomial in S is a product xa = xa11... x
Combinatorial invariance of Stanley-Reisner rings
- 315–318. PROBLEMS OF TORIC MANIFOLDS 15
, 1996
"... Abstract. In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application ” in combinatorics [2, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes. For convenience we recall the notion of a ..."
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Cited by 11 (1 self)
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faces. Now assume we are given a field k and an abstract simplicial complex ∆ on a vertex set V. The Stanley–Reisner ring corresponding to these data is defined as the quotient ring of the polynomial ring k[v1,..., vn]/I, where n = #(V), the vi are the elements of V, and the ideal I is generated
ON THE STANLEY DEPTH OF SQUAREFREE VERONESE IDEALS
, 2009
"... Let K be a field and S = K[x1,...,xn]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth(M), and conjectured that depth(M) ≤ sdepth(M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zhe ..."
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Cited by 12 (4 self)
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Let K be a field and S = K[x1,...,xn]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth(M), and conjectured that depth(M) ≤ sdepth(M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu
ON THE STANLEY DEPTH OF WEAKLY POLYMATROIDAL IDEALS
"... Let K be a field and S = K[x1,..., xn] be the polynomial ring in n variables over the field K. In this paper, it is shown that Stanley’s conjecture holds for I and S/I if I is a product of monomial prime ideals or I is a high enough power of a polymatroidal or a stable ideal generated in a single de ..."
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Cited by 2 (2 self)
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Let K be a field and S = K[x1,..., xn] be the polynomial ring in n variables over the field K. In this paper, it is shown that Stanley’s conjecture holds for I and S/I if I is a product of monomial prime ideals or I is a high enough power of a polymatroidal or a stable ideal generated in a single
STANLEY’S CONJECTURE FOR CRITICAL IDEALS
, 2009
"... Let S = K[x1,..., xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non critical monomial ideals we show the e ..."
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Let S = K[x1,..., xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non critical monomial ideals we show
Stanley Krippner and Allan Combs The Neurophenomenology
"... Michael Winkelman, who is a senior lecturer in the department of anthropology, Arizona State University, and director of its ethnographic field school, has provided a rich overview of the neurophenomenology of shamanism in his book, ..."
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Michael Winkelman, who is a senior lecturer in the department of anthropology, Arizona State University, and director of its ethnographic field school, has provided a rich overview of the neurophenomenology of shamanism in his book,
Stanley depth of squarefree monomial ideals
"... In this paper, we answer a question posed by Y.H. Shen. We prove that if I is an m-generated squarefree monomial ideal in the polynomial ring S = K[x1,..., xn] with K a field, then sdepth I ≥ n − ⌊m/2⌋. The proof is inductive and uses the correspondence between a Stanley decomposition of a monomial ..."
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In this paper, we answer a question posed by Y.H. Shen. We prove that if I is an m-generated squarefree monomial ideal in the polynomial ring S = K[x1,..., xn] with K a field, then sdepth I ≥ n − ⌊m/2⌋. The proof is inductive and uses the correspondence between a Stanley decomposition of a monomial
Results 1 - 10
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135
