scholarly journals On Pythagorean triplet semigroups

2020 ◽  
Vol 26 (4) ◽  
pp. 63-67
Author(s):  
Antoine Mhanna ◽  
Keyword(s):  
Numerical Semigroups ◽  
Apéry Set ◽  
Frobenius Numbers

In this note we explain the two pseudo-Frobenius numbers for \langle m^2-n^2,m^2+n^2,2mn\rangle where m and n are two coprime numbers of different parity. This lets us give an Apéry set for these numerical semigroups.

scholarly journals Numerical Semigroups with a Monotonic Apery Set

2005 ◽  
Vol 55 (3) ◽  
pp. 755-772 ◽  
Author(s):  
J. C. Rosales ◽  
P. A. Garcia-Sanchez ◽  
J. I. Garcia-Garcia ◽  
M. B. Branco
Keyword(s):  
Numerical Semigroups ◽  
Apéry Set

Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes

2015 ◽  
Vol 91 (1) ◽  
pp. 238-259 ◽  
Author(s):  
Mikhail Lepilov ◽  
Joshua O’Rourke ◽  
Irena Swanson
Keyword(s):  
Numerical Semigroups ◽  
Frobenius Numbers

scholarly journals Generalized Strongly Increasing Semigroups

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1370
Author(s):  
E. R. García Barroso ◽  
J. I. García-García ◽  
A. Vigneron-Tenorio
Keyword(s):  
Frobenius Number ◽  
Numerical Semigroups ◽  
New Class ◽  
Frobenius Numbers ◽  
Positive Integers

In this work, we present a new class of numerical semigroups called GSI-semigroups. We see the relations between them and other families of semigroups and we explicitly give their set of gaps. Moreover, an algorithm to obtain all the GSI-semigroups up to a given Frobenius number is provided and the realization of positive integers as Frobenius numbers of GSI-semigroups is studied.

scholarly journals THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA

2017 ◽  
Vol 96 (3) ◽  
pp. 400-411 ◽  
Author(s):  
I. OJEDA ◽  
A. VIGNERON-TENORIO
Keyword(s):  
Semigroup Algebra ◽  
Numerical Semigroups ◽  
Frobenius Numbers ◽  
Affine Semigroups ◽  
Affine Semigroup ◽  
Lattice Ideal ◽  
Apéry Sets

This work generalises the short resolution given by Pisón Casares [‘The short resolution of a lattice ideal’, Proc. Amer. Math. Soc.131(4) (2003), 1081–1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen–Macaulay property for simplicial affine semigroups.

scholarly journals Numerical semigroups with a given set of pseudo-Frobenius numbers

2016 ◽  
Vol 19 (1) ◽  
pp. 186-205 ◽  
Author(s):  
M. Delgado ◽  
P. A. García-Sánchez ◽  
A. M. Robles-Pérez
Keyword(s):  
Partial Order ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Frobenius Numbers

The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.

scholarly journals The genus, Frobenius number and pseudo-Frobenius numbers of numerical semigroups of type 2

2016 ◽  
Vol 146 (5) ◽  
pp. 1081-1090
Author(s):  
Aureliano M. Robles-Pérez ◽  
José Carlos Rosales
Keyword(s):  
Numerical Semigroup ◽  
Sufficient Conditions ◽  
Frobenius Number ◽  
The Other ◽  
Numerical Semigroups ◽  
Frobenius Numbers ◽  
The One ◽  
Necessary And Sufficient ◽  
Positive Integers

We study some questions on numerical semigroups of type 2. On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudo-Frobenius numbers and, moreover, we explicitly build families of such numerical semigroups.

scholarly journals Almost canonical ideals and GAS numerical semigroups

2021 ◽  
pp. 1-24
Author(s):  
Marco D’Anna ◽  
Francesco Strazzanti
Keyword(s):  
Numerical Semigroups
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