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Title: Minimal binomial systems of generators for the ideals of certain monomial curves
Authors: Branco, Manuel B.
Isabel, Colaço
Ignacio, Ojeda
Keywords: Binomial ideal, semigroup ideal, minimal system of generators, determi- nantal ideal, Gr ̈obner basis, indispensability.
Issue Date: Dec-2021
Publisher: MDPI
Citation: Branco, M.B.; Colaço, I. Ojeda, I. Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves. Mathematics 2021, 9, 3204.
Abstract: Let a, b and n > 1 be three positive integers such that a and ∑n−1 j=0 bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by {∑n−1 j=0 bj } ∪ {∑n−1 j=0 bj + a ∑i−2 j=0 bj | i = 2, . . . , n} is determinantal. Moreover, we prove that for n > 3, the ideal I has a unique minimal system of generators if and only if a < b − 1.
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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