On the Stanley depth of squarefree Veronese ideals

Keller, Mitchel T.; Shen, Yi-Huang; Streib, Noah; Young, Stephen J.

doi:10.1007/s10801-010-0249-1

Cited by 16 publications

(31 citation statements)

References 15 publications

(23 reference statements)

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“…. , x n ] for some degrees [4,12], results on the Stanley depth of complete intersection monomial ideals [13,15,22], and CoCoA implementations of the algorithm [10,21].…”

Section: Introductionmentioning

confidence: 99%

Depth and Stanley depth of the edge ideals of square paths and square cycles

Iqbal

Ishaq

Aamir

2017

Communications in Algebra

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ABSTRACT. We develop combinatorial tools to study the relationship between the Stanley depth of a monomial ideal I and the Stanley depth of its compliment, S/I. Using these results we are able to prove that if S is a polynomial ring with at most 5 indeterminates and I is a square-free monomial ideal, then the Stanley depth of S/I is strictly larger than the Stanley depth of I. Using a computer search, we are able to extend this strict inequality up to polynomial rings with at most 7 indeterminates. This partially answers questions asked by Propescu and Qureshi as well as Herzog.

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“…. , x n ] for some degrees [4,12], results on the Stanley depth of complete intersection monomial ideals [13,15,22], and CoCoA implementations of the algorithm [10,21].…”

Section: Introductionmentioning

confidence: 99%

Depth and Stanley depth of the edge ideals of square paths and square cycles

Iqbal

Ishaq

Aamir

2017

Communications in Algebra

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“…The methods of interval partitions of posets have been extended and refined by Keller et al [119] to obtain the following results on the Stanley depth of the squarefree Veronese ideal I n;d which is the ideal of all squarefree monomials in n variables generated in degree d . [76].…”

Section: Special Partitions Of Posetsmentioning

confidence: 99%

“…For our next result we will use the following proposition which can be extracted from the work of Keller et al [119] and Gi et al [76] and as it is summarized in [62].…”

Section: Special Partitions Of Posetsmentioning

confidence: 99%

Monomial Ideals, Computations and Applications

Bigatti¹,

Gimenez²,

Sáenz-de-Cabezón³

2013

Lecture Notes in Mathematics

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“…First we consider Case(1) where the proof idea comes from [10]. We recall the method of Herzog et al [9] for computing the Stanley depth of a squarefree monomial ideal I using posets.…”

Section: Now Let Us Define An Isomorphismmentioning

confidence: 99%