The Apéry Set of a Good Semigroup

2020 ◽  
pp. 79-104 ◽  
Author(s):  
Marco D’Anna ◽  
Lorenzo Guerrieri ◽  
Vincenzo Micale
Keyword(s):  
Apéry Set ◽  
Good Semigroup

Compositions of a numerical semigroup

2019 ◽  
Vol 29 (5) ◽  
pp. 345-350
Author(s):  
Ze Gu
Keyword(s):  
Nonnegative Integer ◽  
Numerical Semigroup ◽  
Apéry Set ◽  
Wilf’S Conjecture

Abstract Given a numerical semigroup S, a nonnegative integer a and m ∈ S ∖ {0}, we introduce the set C(S, a, m) = {s + aw(s mod m) | s ∈ S}, where {w(0), w(1), ⋯, w(m – 1)} is the Apéry set of m in S. In this paper we characterize the pairs (a, m) such that C(S, a, m) is a numerical semigroup. We study the principal invariants of C(S, a, m) which are given explicitly in terms of invariants of S. We also characterize the compositions C(S, a, m) that are symmetric, pseudo-symmetric and almost symmetric. Finally, a result about compliance to Wilf’s conjecture of C(S, a, m) is given.

scholarly journals On the computation of the Apéry set of numerical monoids and affine semigroups

2014 ◽  
Vol 91 (1) ◽  
pp. 139-158 ◽  
Author(s):  
Guadalupe Márquez-Campos ◽  
Ignacio Ojeda ◽  
José M. Tornero
Keyword(s):  
Apéry Set ◽  
Affine 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

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.

Arf good semigroups

2018 ◽  
Vol 17 (10) ◽  
pp. 1850182 ◽  
Author(s):  
Giuseppe Zito
Keyword(s):  
Numerical Semigroup ◽  
Arf Numerical Semigroup ◽  
Good Semigroup ◽  
Arf Semigroups

In this paper, we study the property of the Arf good subsemigroups of [Formula: see text], with [Formula: see text]. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of determining the Arf closure of a set of vectors and of a good semigroup, extending the concept of characters of an Arf numerical semigroup to Arf good semigroups.

The Type of a Good Semigroup and the Almost Symmetric Condition

2019 ◽  
Vol 17 (1) ◽  
Author(s):  
Marco D’Anna ◽  
Lorenzo Guerrieri ◽  
Vincenzo Micale
Keyword(s):  
Good Semigroup
Sign in / Sign up

Export Citation Format

Share Document