Branco, M.B.; Colaço, I.; Ojeda, I. Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves. Mathematics2021, 9, 3204.
Branco, M.B.; Colaço, I.; Ojeda, I. Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves. Mathematics 2021, 9, 3204.
Branco, M.B.; Colaço, I.; Ojeda, I. Minimal Systems of Binomial Generators for the Ideals of Certain Monomial Curves. Mathematics2021, 9, 3204.
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 $\sum_{j=0}^{n-1} b^j$ are relatively prime. In this paper, we prove that the toric ideal $I$ associated to the submonoid of $\mathbb{N}$ generated by $\{\sum_{j=0}^{n-1} b^j\} \cup \{\sum_{j=0}^{n-1} b^j + a\, \sum_{j=0}^{i-2} b^j \mid i = 2, \ldots, n\}$ is determinantal. Moreover, we prove that for $n > 3$, the ideal $I$ has a unique minimal system of generators if and only if $a < b-1$.
Keywords
Binomial ideal; semigroup ideal; minimal systems of generators; determinantal ideal; Gröbner basis; Indispensability
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
