Eliahou number, Wilf function and concentration of a numerical semigroup
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Eliahou number, Wilf function and concentration of a numerical semigroupData de publicació
2022-03-30Editor
Taylor & FrancisISSN
1607-3606; 1727-933XCita bibliogràfica
Patricio Almirón & Julio José Moyano-Fernández (2022) Eliahou number, Wilf function and concentration of a numerical semigroup, Quaestiones MathematicaeTipus de document
info:eu-repo/semantics/articleVersió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have a negative Eliahou ... [+]
We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have a negative Eliahou number in terms of its multiplicity, concentration and Wilf function. Also, we show new examples of numerical semigroups with a negative Eliahou number satisfying the Wilf conjecture. In addition, we introduce the notion of highly dense numerical semigroup; this yields a new family of numerical semigroups satisfying the Wilf conjecture. Moreover, we use the Wilf function of a numerical semigroup to prove that the Eliahou number of a highly dense numerical semigroup is positive under certain additional hypothesis. These results provide new evidences in favour of the Wilf conjecture. [-]
Publicat a
Quaestiones Mathematicae, Vol. 45 (2022)Drets d'accés
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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