Numerical semigroups with concentration two
Identificadores
URI: http://hdl.handle.net/10481/74054Metadatos
Afficher la notice complèteEditorial
Elsevier
Materia
Numerical semigroup Concentration Frobenius number Genus Multiplicity Wilf's conjecture
Date
2021-03-30Referencia bibliográfica
Published version: José C. Rosales, M.B. Branco, Márcio A. Traesel, Numerical semigroups with concentration two, Indagationes Mathematicae, Volume 33, Issue 2, 2022, Pages 303-313, ISSN 0019-3577, [https://doi.org/10.1016/j.indag.2021.07.004]
Patrocinador
project FCT (Fundacao para a Ciencia e a Tecnologia) PTDC/MAT/73544/2006; Junta de Andalucia FQM-343 MTM-2017-84890-PRésumé
We define the concentration of a numerical semigroup S as C(S) = max {next(S)(s) - s vertical bar s is an element of S\{0}} wherein next(S)(s) = min {x is an element of S vertical bar s < x}. In this paper, we study the class of numerical semigroups with concentration 2. We give algorithms to calculate the whole set of this class of semigroups with given multiplicity, genus or Frobenius number. Separately, we prove that this class of semigroups verifies the Wilf's conjecture.