Numerical semigroups with concentration two

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URI: http://hdl.handle.net/10481/74054
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Author
Rosales González, José Carlos
Editorial
Elsevier
Materia
Numerical semigroup
 
Concentration
 
Frobenius number
 
Genus
 
Multiplicity
 
Wilf's conjecture
 
Date
2021-03-30
Referencia 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]
Sponsorship
project FCT (Fundacao para a Ciencia e a Tecnologia) PTDC/MAT/73544/2006; Junta de Andalucia FQM-343 MTM-2017-84890-P
Abstract
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.
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Atribución 3.0 España
Except where otherwise noted, this item's license is described as Atribución 3.0 España