scholarly journals An extension of Wilf’s conjecture to affine semigroups

2017 ◽  
Vol 96 (2) ◽  
pp. 396-408 ◽  
Author(s):  
J. I. García-García ◽  
D. Marín-Aragón ◽  
A. Vigneron-Tenorio
Keyword(s):  
Affine Semigroups ◽  
Wilf’S Conjecture

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

2021 ◽  
Vol 102 (2) ◽  
pp. 340-356
Author(s):  
Tristram Bogart ◽  
John Goodrick ◽  
Kevin Woods
Keyword(s):  
Periodic Behavior ◽  
Presburger Arithmetic ◽  
Affine Semigroups

scholarly journals Unital affine semigroups

2013 ◽  
Vol 439 (7) ◽  
pp. 2106-2113 ◽  
Author(s):  
David W. Kribs ◽  
Jeremy Levick ◽  
Rajesh Pereira
Keyword(s):  
Affine Semigroups

Complementary Bell Numbers: Arithmetical Properties and Wilf’s Conjecture

2013 ◽  
pp. 23-56
Author(s):  
Tewodros Amdeberhan ◽  
Valerio De Angelis ◽  
Victor H. Moll
Keyword(s):  
Bell Numbers ◽  
Wilf’S Conjecture

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 Near-misses in Wilf’s conjecture

2018 ◽  
Vol 98 (2) ◽  
pp. 285-298
Author(s):  
Shalom Eliahou ◽  
Jean Fromentin
Keyword(s):  
Near Misses ◽  
Wilf’S Conjecture

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

2019 ◽  
Vol 78 ◽  
pp. 190-204 ◽  
Author(s):  
Stephan Ramon Garcia ◽  
Christopher O’Neill ◽  
Samuel Yih
Keyword(s):  
Length Distribution ◽  
Numerical Semigroups ◽  
Affine Semigroups

scholarly journals Normality and covering properties of affine semigroups

1999 ◽  
Vol 1999 (510) ◽  
pp. 161-178 ◽  
Author(s):  
Winfried Bruns ◽  
Joseph Gubeladze
Keyword(s):  
Affine Semigroups ◽  
Covering Properties

Measure preserving actions of affine semigroups and patterns

2016 ◽  
Vol 38 (2) ◽  
pp. 473-498 ◽  
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$y\in {\mathcal{O}}_{K}$,$\{x+y,xy\}\subset C_{i}$.

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