Related papers: On permutation numerical semigroups

We report the number of semigroups with 9 elements up to isomorphism or anti-isomorphism to be 52,989,400,714,478 and up to isomorphism to be 105,978,177,936,292. We obtained these results by combining computer search with recently…

In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence…

In this work we introduce the notion of almost-symmetry for generalized numerical semigroups. In addition to the main properties occurring in this new class, we present several characterizations for its elements. In particular we show that…

This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron that classifies the semigroups with given genus (or Frobenius…

We generalize the geometric sequence $\{a^p, a^{p-1}b, a^{p-2}b^2,...,b^p\}$ to allow the $p$ copies of $a$ (resp. $b$) to all be different. We call the sequence $\{a_1a_2a_3\cdots a_p, b_1a_2a_3\cdots a_p, b_1b_2a_3\cdots a_p,\ldots,…

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…

For g $\ge$ 0, let n g denote the number of numerical semi-groups of genus g. A conjecture by Maria Bras-Amor\'os in 2008 states that the inequality n g $\ge$ n g--1 + n g--2 should hold for all g $\ge$ 2. Here we show that such an…

We prove that for every nonempty set $\Sigma$ of integers bigger than $1$, which has at most three elements, there exists a numerical semigroup $T$ and an element $x$ of $T$ such that a natural number $n$ is the number of atoms in a…

In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the root…

A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…

In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $\nu \ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We…

We study how certain invariants of numerical semigroups relate to the number of second kind gaps. Furthermore, given two fixed non-negative integers F and k, we provide an algorithm to compute all the numerical semigroups whose Frobenius…

In this paper we compute the Frobenius number of certain {\em Fibonacci numerical semigroups}, that is, numerical semigroups generated by a set of Fibonacci numbers, in terms of Fibonacci numbers.

We introduce a new way of counting numerical semigroups, namely by their maximum primitive, and show its relation with the counting of numerical semigroups by their Frobenius number. We show that these two ways of counting are M\"obius…

We prove that the type of nearly Gorenstein numerical semigroups minimally generated by $5$ integers is bounded. In particular, if such a semigroup is not almost symmetric, then its type is at most $40$. Finally, we make some considerations…

As a consequence of the classification of finite simple groups, the classification of permutation groups of prime degree is complete, apart from the question of when the natural degree $(q^n-1)/(q-1)$ of ${\rm L}_n(q)$ is prime. We present…

In this paper we give an algorithm for the computation of all the Arf numerical semigroups with a given genus. Moreover, we generalize the concept of genus of a numerical semigroup to good semigroups of $\mathbb{N}^r$ and we give a…

We study numerical semigroups with the property "multiplicity= embedding dimension+1", generated by concatenation of arithmetic sequences.

We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…

We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…