scholarly journals When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three

2015 ◽  
Vol 8 (4) ◽  
pp. 677-694
Author(s):  
Pedro A. García-Sánchez ◽  
Caterina Viola
Keyword(s):  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Catenary Degree

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 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.

Proportionally modular numerical semigroups with embedding dimension three

2014 ◽  
Vol 84 (3-4) ◽  
pp. 319-332 ◽  
Author(s):  
AURELIANO M. ROBLES-PEREZ ◽  
JOSE CARLOS ROSALES
Keyword(s):  
Numerical Semigroups ◽  
Embedding Dimension

Delta sets for nonsymmetric numerical semigroups with embedding dimension three

2018 ◽  
Vol 30 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Pedro A. García-Sánchez ◽  
David Llena ◽  
Alessio Moscariello
Keyword(s):  
Fast Algorithm ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Delta Set

Abstract We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroup with embedding dimension three. We also characterize the sets of integers that are the Delta set of a numerical semigroup of this kind.

scholarly journals On the number of L-shapes in embedding dimension four numerical semigroups

2015 ◽  
Vol 338 (12) ◽  
pp. 2168-2178
Author(s):  
F. Aguiló-Gost ◽  
P.A. García-Sánchez ◽  
D. Llena
Keyword(s):  
Numerical Semigroups ◽  
Embedding Dimension

Numerical semigroups with embedding dimension three

2004 ◽  
Vol 83 (6) ◽  
pp. 488-496 ◽  
Author(s):  
J. C. Rosales ◽  
P. A. Garc�a-S�anchez
Keyword(s):  
Numerical Semigroups ◽  
Embedding Dimension

scholarly journals Wilf’s conjecture for numerical semigroups with large second generator

2020 ◽  
pp. 2150197
Author(s):  
Dario Spirito
Keyword(s):  
Quadratic Function ◽  
Numerical Semigroups ◽  
Embedding Dimension ◽  
Wilf’S Conjecture

We study Wilf’s conjecture for numerical semigroups [Formula: see text] such that the second least generator [Formula: see text] of [Formula: see text] satisfies [Formula: see text], where [Formula: see text] is the conductor and [Formula: see text] the multiplicity of [Formula: see text]. In particular, we show that for these semigroups Wilf’s conjecture holds when the multiplicity is bounded by a quadratic function of the embedding dimension.

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