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

Guadalupe Márquez-Campos; Ignacio Ojeda; José M. Tornero

doi:10.1007/s00233-014-9631-y

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

Semigroup Forum ◽

10.1007/s00233-014-9631-y ◽

2014 ◽

Vol 91 (1) ◽

pp. 139-158 ◽

Cited By ~ 4

Author(s):

Guadalupe Márquez-Campos ◽

Ignacio Ojeda ◽

José M. Tornero

Keyword(s):

Apéry Set ◽

Affine Semigroups

Download Full-text

Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

Semigroup Forum ◽

10.1007/s00233-021-10164-3 ◽

2021 ◽

Vol 102 (2) ◽

pp. 340-356

Author(s):

Tristram Bogart ◽

John Goodrick ◽

Kevin Woods

Keyword(s):

Periodic Behavior ◽

Presburger Arithmetic ◽

Affine Semigroups

Download Full-text

Unital affine semigroups

Linear Algebra and its Applications ◽

10.1016/j.laa.2013.06.005 ◽

2013 ◽

Vol 439 (7) ◽

pp. 2106-2113 ◽

Cited By ~ 1

Author(s):

David W. Kribs ◽

Jeremy Levick ◽

Rajesh Pereira

Keyword(s):

Affine Semigroups

Download Full-text

Compositions of a numerical semigroup

Discrete Mathematics and Applications ◽

10.1515/dma-2019-0032 ◽

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.

Download Full-text

Factorization length distribution for affine semigroups I: Numerical semigroups with three generators

European Journal of Combinatorics ◽

10.1016/j.ejc.2019.01.009 ◽

2019 ◽

Vol 78 ◽

pp. 190-204 ◽

Cited By ~ 2

Author(s):

Stephan Ramon Garcia ◽

Christopher O’Neill ◽

Samuel Yih

Keyword(s):

Length Distribution ◽

Numerical Semigroups ◽

Affine Semigroups

Download Full-text

Almost everywhere convergence of multiple operator averages for affine semigroups

Acta Scientiarum Mathematicarum ◽

10.14232/actasm-016-510-0 ◽

2018 ◽

Vol 84 (34) ◽

pp. 509-554 ◽

Cited By ~ 1

Author(s):

Takeshi Yoshimoto

Keyword(s):

Almost Everywhere Convergence ◽

Almost Everywhere ◽

Affine Semigroups ◽

Multiple Operator

Download Full-text

Normality and covering properties of affine semigroups

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crll.1999.044 ◽

1999 ◽

Vol 1999 (510) ◽

pp. 161-178 ◽

Cited By ~ 12

Author(s):

Winfried Bruns ◽

Joseph Gubeladze

Keyword(s):

Affine Semigroups ◽

Covering Properties

Download Full-text

Measure preserving actions of affine semigroups and patterns

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2016.39 ◽

2016 ◽

Vol 38 (2) ◽

pp. 473-498 ◽

Cited By ~ 3

Author(s):

VITALY BERGELSON ◽

JOEL MOREIRA

Keyword(s):

Ergodic Theorem ◽

Affine Group ◽

General Situation ◽

Finite Partition ◽

Integral Domains ◽

New Approach ◽

Ring Of Integers ◽

Affine Semigroups ◽

Multiplicative Groups ◽

Measure Preserving Actions

Ergodic and combinatorial results obtained in Bergelson and Moreira [Ergodic theorem involving additive and multiplicative groups of a field and$\{x+y,xy\}$patterns.Ergod. Th. & Dynam. Sys.to appear, published online 6 October 2015, doi:10.1017/etds.2015.68], involved measure preserving actions of the affine group of a countable field$K$. In this paper, we develop a new approach, based on ultrafilter limits, which allows one to refine and extend the results obtained in Bergelson and Moreira,op. cit., to a more general situation involving measure preserving actions of thenon-amenableaffine semigroups of a large class of integral domains. (The results and methods in Bergelson and Moreira,op. cit., heavily depend on the amenability of the affine group of a field.) Among other things, we obtain, as a corollary of an ultrafilter ergodic theorem, the following result. Let$K$be a number field and let${\mathcal{O}}_{K}$be the ring of integers of$K$. For any finite partition$K=C_{1}\cup \cdots \cup C_{r}$, there exists$i\in \{1,\ldots ,r\}$such that, for many$x\in K$and many$y\in {\mathcal{O}}_{K}$,$\{x+y,xy\}\subset C_{i}$.

Download Full-text