Research Article

Positioned numerical semigroups

Published in: Quaestiones Mathematicae
Volume 44 , issue 5 , 2021 , pages: 679–691

DOI: 10.2989/16073606.2020.1742245

Author(s): M.B. Branco , Portugal , M.C. Faria , Portugal , J.C. Rosales , Spain

Keywords: 20M14 , 11D07 , 20M14 , 11D07

Abstract

A numerical semigroup S is positioned if for all s ∈ ℕ\S we have that F(S) + m(S) − s ∈ S. In this paper, we give algorithms to compute the set of positioned semigroups and a criterium to check whether S is or not is positioned. Furthermore, we prove the Wilf’s conjecture for this type of numerical semigroups.

« On some new Gaussian hypergeometric summation formulae with applications

Generating integer polynomials from X ² and X ³ using function composition: a study of subnearrings of (ℤ[X], +, ◦) »