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Depth and Stanley depth of multigraded modules
"... Abstract. We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element. ..."
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Abstract. We study the behavior of depth and Stanley depth along short exact sequences of multigraded modules and under reduction modulo an element.
INTERVAL PARTITIONS AND STANLEY DEPTH
, 2008
"... In this paper, we answer a question posed by Herzog, Vladoiu, ..."
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In this paper, we answer a question posed by Herzog, Vladoiu,
AN INEQUALITY BETWEEN DEPTH AND STANLEY DEPTH
, 2009
"... 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. ..."
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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.
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 Smodule M, denoted sdepth(M), and conjectured that depth(M) ≤ sdepth(M) for all finitely generated Smodules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zhe ..."
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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 Smodule M, denoted sdepth(M), and conjectured that depth(M) ≤ sdepth(M) for all finitely generated Smodules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when M = I/J with J ⊂ I being monomial Sideals. Specifically, their method associates M with a partially ordered set. In this paper we take advantage of this association by using combinatorial tools to analyze squarefree Veronese ideals in S. In particular, if In,d is the squarefree Veronese ideal generated by all squarefree monomials of ( n) degree d, we show that if 1 ≤ d ≤ n < 5d + 4, then sdepth(In,d) = d+1 / ( n) d + d, and ⌊ ( n) if d ≥ 1 and n ≥ 5d + 4, then d + 3 ≤ sdepth(In,d) ≤ d+1 / ( n) d + d.
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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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 irreducible monomial ideals of S.
STANLEY DEPTH OF MULTIGRADED MODULES
, 2008
"... The Stanley’s Conjecture on CohenMacaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, SoleymanJahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables. ..."
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The Stanley’s Conjecture on CohenMacaulay multigraded modules is studied especially in dimension 2. In codimension 2 similar results were obtained by Herzog, SoleymanJahan and Yassemi. As a consequence of our results Stanley’s Conjecture holds in 5 variables.