The $$\mathrm {v}$$-number of monomial ideals

Kamalesh, Saha,; Sengupta, Indranath

doi:10.1007/s10801-022-01137-y

Cited by 8 publications

(4 citation statements)

References 21 publications

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“…The following result [38,Proposition 3.11] of Saha and Sengupta provides an useful general method to bound v(I) from above, when I is a monomial ideal.…”

Section: The V-number Of Ideals With Linear Powersmentioning

confidence: 99%

“…In [30], the authors studied the behaviour of the v-number of monomial ideals under polarization. They showed that v(I ℘ ) ≤ v(I) and equality holds in some special cases.…”

Section: Reduction To the Squarefree Casementioning

confidence: 99%

“…The concept of v-number was introduced by Cooper et all in [10], and further studied in [1,8,26,32,33,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…We denote the set of associated primes of I by Ass(I), and by Max(I) the set of associated primes of I that are maximal with respect to the inclusion. The concept of v-number was introduced in [7], and further studied in [1,3,5,17,20,25,26,29,30,32]. Let I ⊂ S be a graded ideal and let p ∈ Ass(I).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Ficarra

2023

Journal of Algebra

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“…The following result [38,Proposition 3.11] of Saha and Sengupta provides an useful general method to bound v(I) from above, when I is a monomial ideal.…”

Section: The V-number Of Ideals With Linear Powersmentioning

confidence: 99%

“…In [30], the authors studied the behaviour of the v-number of monomial ideals under polarization. They showed that v(I ℘ ) ≤ v(I) and equality holds in some special cases.…”

Section: Reduction To the Squarefree Casementioning

confidence: 99%

“…The concept of v-number was introduced by Cooper et all in [10], and further studied in [1,8,26,32,33,38,39].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Ficarra

2023

Journal of Algebra

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The v-number and Castelnuovo–Mumford regularity of graphs

Civan

2022

J Algebr Comb

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Connected domination in graphs and v-numbers of binomial edge ideals

Jaramillo-Velez,

Seccia

2023

Collect. Math.

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The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and originally motivated by problems in algebraic coding theory. In this paper we study the case of binomial edge ideals and we establish a significant connection between their v-numbers and the concept of connected domination in graphs. More specifically, we prove that the localization of the v-number at one of the minimal primes of the binomial edge ideal $$J_G$$ J G of a graph G coincides with the connected domination number of the defining graph, providing a first algebraic description of the connected domination number. As an immediate corollary, we obtain a sharp combinatorial upper bound for the v-number of binomial edge ideals of graphs. Lastly, building on some known results on edge ideals, we analyse how the v-number of $$J_G$$ J G behaves under Gröbner degeneration when G is a closed graph.

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The $$\mathrm {v}$$-number of monomial ideals

Cited by 8 publications

References 21 publications

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

Vector-spread monomial ideals and Eliahou–Kervaire type resolutions

The v-number and Castelnuovo–Mumford regularity of graphs

Connected domination in graphs and v-numbers of binomial edge ideals

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