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2019•MathematicsOpen access

Extremal Betti Numbers of t-Spread Strongly Stable Ideals

Luca Amata, Marilena Crupı

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Abstract

Let K be a field and let S = K [ x 1 , ⋯ , x n ] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread strongly stable ideals, where t is an integer ≥ 1 . A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the t-spread strongly stable ideals with the maximal number of extremal Betti numbers when t = 2 .

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Let K be a field and let S = K [ x 1 , ⋯ , x n ] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread strongly stable ideals, where t is an integer ≥ 1 . A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the t-spread strongly stable ideals with the maximal number of extremal Betti numbers when t = 2 .

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Available abstract

Let K be a field and let S = K [ x 1 , ⋯ , x n ] be a polynomial ring over K. We analyze the extremal Betti numbers of special squarefree monomial ideals of S known as the t-spread strongly stable ideals, where t is an integer ≥ 1 . A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the t-spread strongly stable ideals with the maximal number of extremal Betti numbers when t = 2 .

Key concepts: Betti number, Square-free integer, Mathematics, Monomial, Polynomial ring, Combinatorics, Monomial ideal, Integer (computer science)

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