On robustness and related properties on toric ideals

García-Marco, Ignacio; Tatakis, Christos

doi:10.1007/s10801-022-01162-x

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Complete Intersection and Strongly Robustness1

Introduction1

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2023

2024

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Cited by 4 publications

(2 citation statements)

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“…Thus, I T is a T [s] -robust ideal and [s] ∈ ∆ T . The fact that the toric ideal of a monomial curve is not robust for s ≥ 3, thus also not strongly robust, was also noticed in [12,Corollary 4.17].…”

Section: Complete Intersection and Strongly Robustnessmentioning

confidence: 81%

“…The classical example of strongly robust ideals are the Lawrence ideals, see [21,Chapter 7]. There are several articles in the literature studying robust related properties of ideals; see [2,3,10,11,22] for robust ideals, [4,5] for robust toric ideals, [12,24] for generalized robust toric ideals and [14,17,19,20,21,23] for strongly robust toric ideals.…”

Section: Introductionmentioning

confidence: 99%

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On the strongly robust property of toric ideals

Kosta

Thoma²,

Vlădoiu³

2023

Journal of Algebra

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Section: Complete Intersection and Strongly Robustnessmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

On the strongly robust property of toric ideals

Kosta

Thoma²,

Vlădoiu³

2023

Journal of Algebra

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The strongly robust simplicial complex of monomial curves

Kosta,

Thoma,

Vladoiu

2024

J Algebr Comb

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To every simple toric ideal $$I_T$$ I T one can associate the strongly robust simplicial complex $$\Delta _T$$ Δ T , which determines the strongly robust property for all ideals that have $$I_T$$ I T as their bouquet ideal. We show that for the simple toric ideals of monomial curves in $$\mathbb {A}^{s}$$ A s , the strongly robust simplicial complex $$\Delta _T$$ Δ T is either $$\{\emptyset \}$$ { ∅ } or contains exactly one 0-dimensional face. In the case of monomial curves in $$\mathbb {A}^{3}$$ A 3 , the strongly robust simplicial complex $$\Delta _T$$ Δ T contains one 0-dimensional face if and only if the toric ideal $$I_T$$ I T is a complete intersection ideal with exactly two Betti degrees. Finally, we provide a construction to produce infinitely many strongly robust ideals with bouquet ideal the ideal of a monomial curve and show that they are all produced this way.

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