scholarly journals Presentations of a numerical semigroup

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Belgin Özer ◽  
Sibel Kanbay
Keyword(s):  
Complete Intersection ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Catenary Degree ◽  
Minimal Presentations

In this paper, we mainly study the minimal presentations of numerical semigroups. Moreover, we examine the concept of gluing, complete intersection, catenary degree, elasticity of some numerical semigroups.  

scholarly journals Measuring primality in numerical semigroups with embedding dimension three

2015 ◽  
Vol 15 (01) ◽  
pp. 1650007 ◽  
Author(s):  
S. T. Chapman ◽  
P. A. García-Sánchez ◽  
Z. Tripp ◽  
C. Viola
Keyword(s):  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Catenary Degree

In this paper, we find the ω-value of the generators of any numerical semigroup with embedding dimension three. This allows us to determine all possible orderings of the ω-values of the generators. In addition, we relate the ω-value of the numerical semigroup to its catenary degree.

scholarly journals Isolated factorizations and their applications in simplicial affine semigroups

2019 ◽  
Vol 19 (05) ◽  
pp. 2050082 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
Andrés Herrera-Poyatos
Keyword(s):  
Complete Intersection ◽  
Minimal Element ◽  
Numerical Semigroups ◽  
Commutative Monoid ◽  
Generalize Formula ◽  
Affine Semigroups ◽  
Minimal Presentations ◽  
Minimal Generators

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups. We also generalize [Formula: see text]-rectangular numerical semigroups to the context of simplicial affine semigroups and study their isolated factorizations. As a consequence of our results, we characterize those complete intersection simplicial affine semigroups with only one Betti minimal element in several ways. Moreover, we define Betti sorted and Betti divisible simplicial affine semigroups and characterize them in terms of gluings and their minimal presentations. Finally, we determine all the Betti divisible numerical semigroups, which turn out to be those numerical semigroups that are free for any arrangement of their minimal generators.

scholarly journals Factoring in Embedding Dimension Three Numerical Semigroups

10.37236/410 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
F. Aguiló-Gost ◽  
P. A. García-Sánchez
Keyword(s):  
Numerical Semigroup ◽  
Main Tool ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Catenary Degree

Let us consider a $3$-numerical semigroup $S=\langle{a,b,N}\rangle$. Given $m\in S$, the triple $(x,y,z)\in\mathbb{N}^3$ is a factorization of $m$ in $S$ if $xa+yb+zN=m$. This work is focused on finding the full set of factorizations of any $m\in S$ and as an application we compute the catenary degree of $S$. To this end, we relate a 2D tessellation to $S$ and we use it as a main tool.

scholarly journals Minimal genus of a multiple and Frobenius number of a quotient of a numerical semigroup

2015 ◽  
Vol 25 (06) ◽  
pp. 1043-1053 ◽  
Author(s):  
Francesco Strazzanti
Keyword(s):  
Positive Integer ◽  
Numerical Semigroup ◽  
Frobenius Number ◽  
Numerical Semigroups ◽  
Minimal Genus

Given two numerical semigroups S and T and a positive integer d, S is said to be one over d of T if S = {s ∈ ℕ | ds ∈ T} and in this case T is called a d-fold of S. We prove that the minimal genus of the d-folds of S is [Formula: see text], where g and f denote the genus and the Frobenius number of S. The case d = 2 is a problem proposed by Robles-Pérez, Rosales, and Vasco. Furthermore, we find the minimal genus of the symmetric doubles of S and study the particular case when S is almost symmetric. Finally, we study the Frobenius number of the quotient of some families of numerical semigroups.

scholarly journals Numerical semigroups in a problem about cost-effective transport

2017 ◽  
Vol 29 (2) ◽  
pp. 329-345 ◽  
Author(s):  
Aureliano M. Robles-Pérez ◽  
José Carlos Rosales
Keyword(s):  
Nonnegative Integer ◽  
Numerical Semigroup ◽  
Cost Effective ◽  
Numerical Semigroups ◽  
Integer Coefficients ◽  
Effective Transport ◽  
System Of Inequalities ◽  
Algorithmic Process

AbstractLet ${{\mathbb{N}}}$ be the set of nonnegative integers. A problem about how to transport profitably an organized group of persons leads us to study the set T formed by the integers n such that the system of inequalities, with nonnegative integer coefficients,$a_{1}x_{1}+\cdots+a_{p}x_{p}<n<b_{1}x_{1}+\cdots+b_{p}x_{p}$has at least one solution in ${{\mathbb{N}}^{p}}$. We will see that ${T\cup\{0\}}$ is a numerical semigroup. Moreover, we will show that a numerical semigroup S can be obtained in this way if and only if ${\{a+b-1,a+b+1\}\subseteq S}$, for all ${a,b\in S\setminus\{0\}}$. In addition, we will demonstrate that such numerical semigroups form a Frobenius variety and we will study this variety. Finally, we show an algorithmic process in order to compute T.

scholarly journals Classes of complete intersection numerical semigroups

2013 ◽  
Vol 88 (2) ◽  
pp. 453-467 ◽  
Author(s):  
Marco D’Anna ◽  
Vincenzo Micale ◽  
Alessio Sammartano
Keyword(s):  
Complete Intersection ◽  
Numerical Semigroups

scholarly journals The Numerical Semigroup of Phrases' Lengths in a Simple Alphabet

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Aureliano M. Robles-Pérez ◽  
José Carlos Rosales
Keyword(s):  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Starting Point ◽  
The Family

Let𝒜be an alphabet with two elements. Considering a particular class of words (the phrases) over such an alphabet, we connect with the theory of numerical semigroups. We study the properties of the family of numerical semigroups which arise from this starting point.

scholarly journals Parametrizing Arf numerical semigroups

2017 ◽  
Vol 16 (11) ◽  
pp. 1750209 ◽  
Author(s):  
P. A. García-Sánchez ◽  
B. A. Heredia ◽  
H. İ. Karakaş ◽  
J. C. Rosales
Keyword(s):  
Numerical Semigroup ◽  
Frobenius Number ◽  
Numerical Semigroups ◽  
Arf Numerical Semigroup

We present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical semigroups with fixed Frobenius number and multiplicity up to 7.

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