Hilbert series and Hilbert depth of squarefree Veronese ideals

Ge, Mingwei; Lin, Jiayuan; Wang, Yulan

doi:10.1016/j.jalgebra.2011.07.027

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“…In the standard graded setting, the Hilbert depth of the powers of the maximal ideals [BKU11] and squarefree Veronese ideals [GLW11a] have been calculated and their relation has been studied [GLW11b], from combinatorial point of view. Except for these, the Hilbert depth of many interesting graded objects remains unknown.…”

Section: Introductionmentioning

confidence: 99%

Lexsegment ideals of Hilbert depth 1

Shen¹

2012

Preprint

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Let I ⊂ S = K[x 1 , . . . , xn] be a lexsegment ideal, generated by monomials of degree d. The main aim of this paper is to characterize when the Hilbert depth of I will be 1, in the standard graded case. In addition to this, we will give an estimate of depth of squarefree monomial ideals, generalizing a result of Popescu [Pop12]. We will also show that Stanley conjecture holds for squarefree stable ideals, in the multigraded case.

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Section: Introductionmentioning

confidence: 99%

Lexsegment ideals of Hilbert depth 1

Shen¹

2012

Preprint

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The relevance of Freiman’s theorem for combinatorial commutative algebra

2018

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Freiman's theorem gives a lower bound for the cardinality of the doubling of a finite set in R n . In this paper we give an interpretation of his theorem for monomial ideals and their fiber cones. We call a quasi-equigenerated monomial ideal a Freiman ideal, if the set of its exponent vectors achieves Freiman's lower bound for its doubling. Algebraic characterizations of Freiman ideals are given, and finite simple graphs are classified whose edge ideals or matroidal ideals of its cycle matroids are Freiman ideals.2010 Mathematics Subject Classification. Primary 13C99; Secondary 13A15, 13E15, 13H05, 13H10.

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Hilbert series and Hilbert depth of squarefree Veronese ideals

Abstract: In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring.

Cited by 2 publications

References 15 publications

Lexsegment ideals of Hilbert depth 1

Lexsegment ideals of Hilbert depth 1

The relevance of Freiman’s theorem for combinatorial commutative algebra

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