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Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves

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Let a,b and n>1 be three positive integers such that a and ∑j=0n−1bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid… Click to show full abstract

Let a,b and n>1 be three positive integers such that a and ∑j=0n−1bj are relatively prime. In this paper, we prove that the toric ideal I associated to the submonoid of N generated by {∑j=0n−1bj}∪{∑j=0n−1bj+a∑j=0i−2bj∣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

Keywords: minimal systems; ideals certain; certain monomial; binomial generators; generators ideals; systems binomial

Journal Title: Mathematics
Year Published: 2021

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