Monomial ideals with 3-linear resolutions

Morales, Marcel; Nejad, Abbas Nasrollah; Pour, Ali Akbar Yazdan; Zaare-Nahandi, Rashid

doi:10.5802/afst.1428

Cited by 13 publications

(17 citation statements)

References 7 publications

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“…It is well-known that, for n ≥ d the ideal I (C n,d ) has a d-linear resolution (see e.g. [14,Example 2.12]). If C is a d-uniform clutter on [n], we defineC, the complement of C, to bē…”

Section: Preliminariesmentioning

confidence: 99%

“…However, the converse is still an open question. The definition of chordality given in [14] imitates Dirac's characterization of chordal graphs. It is required that the clutter admits a simplicial order.…”

Section: Introductionmentioning

confidence: 99%

“…

Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field.

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confidence: 99%

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Simplicial orders and chordality

et al. 2016

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Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. We show that any Betti sequence of an ideal with linear resolution appears as the Betti sequence of the circuit ideal of such a chordal clutter. Associated with any simplicial order is a sequence of integers which we call the λ-sequence of the chordal clutter. All possible λ-sequences are characterized. They are intimately related to the Hilbert function of a suitable standard graded K-algebra attached to the chordal clutter. By the λ-sequence of a chordal clutter we determine other numerical invariants of the circuit ideal, such as the h-vector and the Betti numbers.2010 Mathematics Subject Classification. Primary 13D02, 13P20; Secondary 05E45, 05C65.

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“…It is well-known that, for n ≥ d the ideal I (C n,d ) has a d-linear resolution (see e.g. [14,Example 2.12]). If C is a d-uniform clutter on [n], we defineC, the complement of C, to bē…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simplicial orders and chordality

et al. 2016

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“…It is well-known that for n ≥ d the ideal I (C n,d ) has a d-linear resolution (see e.g. [18,Example 2.12]).…”

Section: Simplicial Complexesmentioning

confidence: 99%

Decomposable clutters and a generalization of Simon's conjecture

2019

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“…One can check that I(C n,d ) has d-linear resolution (see also [MNYZ,Example 2.12]). If C is a d-uniform clutter on [n], we defineC, the complement of C, to bē…”

Section: Clutters and Clique Complexesmentioning

confidence: 99%

Regularity and Free Resolution of Ideals Which Are Minimal To $d$-Linearity

Morales¹,

Pour²,

Zaare-Nahandi³

2016

MATH. SCAND.

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Toward a partial classification of monomial ideals with d-linear resolution, in this paper, some classes of d-uniform clutters which do not have linear resolution, but every proper subclutter of them has a d-linear resolution, are introduced and the regularity and Betti numbers of circuit ideals of such clutters are computed. Also, it is proved that for given two d-uniform clutters C1, C2, the CastelnuovoMumford regularity of the ideal I(C1 ∪ C2) is equal to the maximum of regularities of I(C1) and I(C2), whenever V (C1) ∩ V (C2) is a clique or SC(C1) ∩ SC(C2) = ∅.As applications, alternative proofs are given for Fröberg's Theorem on linearity of edge ideal of graphs with chordal complement as well as for linearity of generalized chordal hypergraphs defined by Emtander. Finally, we find minimal free resolutions of the circuit ideal of a triangulation of a pseudo-manifold and a homology manifold explicitly.

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Monomial ideals with 3-linear resolutions

Cited by 13 publications

References 7 publications

Simplicial orders and chordality

Simplicial orders and chordality

Decomposable clutters and a generalization of Simon's conjecture

Regularity and Free Resolution of Ideals Which Are Minimal To $d$-Linearity

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