Asymptotic behavior of Markov complexity

Shmuel Onn; Apostolos Thoma; Marius Vladoiu

doi:10.1016/j.jpaa.2023.107589

Asymptotic behavior of Markov complexity

Shmuel Onn, Apostolos Thoma, Marius Vladoiu

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let A be any integer m×n matrix of rank d. We prove that the Markov and Graver complexities of A may be arbitrarily large for n≥4 and d≤n−2. In contrast, we show they are bounded in terms of n and the largest absolute value a of any entry of A.

Original language	English
Article number	107589
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	6
DOIs	https://doi.org/10.1016/j.jpaa.2023.107589
State	Published - Jun 2024

Keywords

Graver basis
Lawrence liftings
Markov complexity
Toric ideals

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2023.107589

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title = "Asymptotic behavior of Markov complexity",

abstract = "Let A be any integer m×n matrix of rank d. We prove that the Markov and Graver complexities of A may be arbitrarily large for n≥4 and d≤n−2. In contrast, we show they are bounded in terms of n and the largest absolute value a of any entry of A.",

keywords = "Graver basis, Lawrence liftings, Markov complexity, Toric ideals",

author = "Shmuel Onn and Apostolos Thoma and Marius Vladoiu",

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year = "2024",

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AU - Vladoiu, Marius

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AB - Let A be any integer m×n matrix of rank d. We prove that the Markov and Graver complexities of A may be arbitrarily large for n≥4 and d≤n−2. In contrast, we show they are bounded in terms of n and the largest absolute value a of any entry of A.

KW - Graver basis

KW - Lawrence liftings

KW - Markov complexity

KW - Toric ideals

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JO - Journal of Pure and Applied Algebra

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Asymptotic behavior of Markov complexity

Abstract

Keywords

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