Minimal binomial systems of generators for the ideals of certain monomial curves

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.