Related papers: Numerical semigroups with embedding dimension thre…
This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three…
In this paper we present the set of saturated numerical semigroups with prime multiplicity. We also characterize the catenary degree of these semigroups that we acquire. The catenary degree of a numerical semigroup is the variant which…
The delta set of a numerical semigroup $S$, denoted $\Delta(S)$, is a factorization invariant that measures the complexity of the sets of lengths of elements in $S$. We study the following problem: Which finite sets occur as the delta set…
We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.
Given a numerical semigroup $S = < a_1, a_2,..., a_t>$ and $s\in S$, we consider the factorization $s = c_1 a_1 + c_2 a_2 +... + c_t a_t$ where $c_i\ge0$. Such a factorization is {\em maximal} if $c_1+c_2+...+c_t$ is a maximum over all such…
We characterize semigroups in $\{0,1,2,\ldots\}$ of matricial dimension $2$ and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonely has matricial dimension at most $2$.
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound…
We study numerical semigroups with the property "multiplicity= embedding dimension+1", generated by concatenation of arithmetic sequences.
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…
The catenary degree is an invariant that measures the distance between factorizations of elements within a numerical semigroup. In general, all possible catenary degrees of the elements of the numerical semigroups occur as the catenary…
Let $S\subseteq \mathbb N^p$ be a semigroup, any $P\subseteq S$ is an ideal of $S$ if $P+S\subseteq P$, and an $I(S)$-semigroup is the affine semigroup $P\cup \{0\}$, with $P$ an ideal of $S$. We characterise the $I(S)$-semigroups and the…
Attached to a singular analytic curve germ in $d$-space is a numerical semigroup: a subset $S$ of the non-negative integers which is closed under addition and whose complement isfinite. Conversely, associated to any numerical semigroup $S$…
Let $S$ and $\Delta$ be numerical semigroups. A numerical semigroup $S$ is an $\mathbf{I}(\Delta)$-{\it semigroup} if $S\backslash \{0\}$ is an ideal of $\Delta$. We will denote by $\mathcal{J}(\Delta)=\{S \mid S \text{ is an…
This paper determines almost symmetric numerical semigroups with maximal reduced type completely. In addition, this paper classifies MED-semigroups with maximal reduced type.
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 develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. Previous methods of comparable strength worked only for embedding dimension three or under very specific conditions. We…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…
Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in $\{m,m+1,\ldots, 2m-1\}.$ In this work, packed numerical semigroups are used to built the…
In this paper, we consider the following question: "given the multiplicity $m$ and embedding dimension $e$ of a numerical semigroup $S$, what can be said about the cardinality $\eta$ of a minimal presentation of $S$?" We approach this…
Given two numerical semigroups $S$ and $T$ we say that $T$ is a multiple of $S$ if there exists an integer $d \in \mathbb{N} \setminus \{0\}$ such that $S = \{x \in \mathbb{N} \mid d x \in T\}$. In this paper we study the family of…