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Asymptotic behaviour of integer programming and the $\text{v}$-function of a graded filtration

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arxiv 2403.08435 v7 pith:BYXACGWO submitted 2024-03-13 math.AC math.CO

Antonino Ficarra , Emanuele Sgroi This is my paper · ORCID
classification math.ACmath.CO
keywords functiontextasymptoticbehaviourfiltrationgradedintegermathcal
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abstract

The $\text{v}$-function of a graded filtration $\mathcal{I}=\{I_{[k]}\}_{k\ge0}$ is introduced. Under the assumption that $\mathcal{I}$ is Noetherian, we prove that the $\text{v}$-function $\text{v}(I_{[k]})$ is an eventually quasi-linear function. This result applies to several situations, including ordinary powers, and integral closures of ordinary powers, among others. As another application, we investigate the asymptotic behaviour of certain integer programming problems. Finally, we present the \textit{Macaulay2} package $\texttt{VNumber}$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The homological shift algebra of a monomial ideal

    math.AC 2024-12 conditional novelty 7.0 of 10

    For monomial ideals with linear powers, the homological shift algebra is a finitely generated Rees module, making regularity, depth, associated primes, v-number, and Golodness of homological shift ideals eventually li...

  2. Comparison of stability indices of powers of graded ideals

    math.AC 2025-05 accept novelty 6.0 of 10

    The paper proves that astab(I)=1 for every graded ideal in dimension two with vstab(I) arbitrary, and constructs ideals realizing every pair (astab(I), vstab(I))=(a,b) in higher dimension.

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