arXiv subjects

Laura González

Publications and source records attributed to Laura González.

4 recordsLinked to original sources

arXiv2026

Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring

We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra homomorphism. Up to constant coefficients, determined by some specific linear systems with binomial entries, we describe their minimal generating polynomial sets. The advantage of our family with respect to some previous work is, on the one hand, the explicit description of the generating sets and, on the other hand, the simplicity of the exponents of the aforementioned quasi-monomial homomorphism. We also provide a code in Python which states and solves the linear systems that lead to a complete description of the minimal generating sets with a "Gröbner-free" approach.

math.AC↗

arXiv2026

Binomial determinants: some closed formulae

This paper is intended to give closed formulae for binomial determinants with consecutive or almost consecutive rows or columns, as well as calculating the generator of left nullspaces defined by some binomial matrices. In the meantime, we reprove, by different means, the positivity of binomial determinants shown by Gessel and Viennot.

math.CO↗

arXiv2026

Prime ideals of Moh and the characteristic of the field

We reprove and generalize a result of Moh which gives a lower bound on the minimal number of generators of an ideal in a power series ring in three variables x,y,z over a field k. As a consequence, in each characteristic of the field k, we obtain a minimal generating set for the prime ideal P of Moh corresponding to n=3. We deduce that the minimal number of generators of P might decrease depending on the characteristic of k. This contradicts a statement of Sally and leaves as an open problem to find families of prime ideals in the power series ring in the variables x,y,z with an unbounded minimal number of generators, when k has characteristic other than zero. Finally, we show that these minimal generating sets of P are standard basis with the negative degree reverse lexicographic order.

math.AC↗

arXiv2024

Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers

Let $S$ be the numerical semigroup generated by three consecutive numbers $a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$ whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of $S$ in terms of the length and the denumerant. By using Apéry sets and Betti elements we are able to extend some results, first obtained by elementary means.

math.CO↗