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Problems in numerical semigroups

Abstract : The thesis is made up of two parts. We study in the first part Wilf’s conjecture for numerical semigroups. We give an equivalent form of Wilf’s conjecture in terms of the Apéry set, embedding dimension and multiplicity of a numerical semigroup. We also give an affirmative answer for the conjecture in certain cases. In the second part, we consider a class of almost arithmetic numerical semigroups and give for this class of semigroups explicit formulas for the Apéry set, the Frobenius number, the genus and the pseudo-Frobenius numbers. We also characterize the symmetric (resp. pseudo-symmetric) numerical semigroups for this class of numerical semigroups.
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Submitted on : Tuesday, April 17, 2018 - 2:59:06 PM
Last modification on : Wednesday, November 3, 2021 - 9:18:30 AM


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  • HAL Id : tel-01672101, version 2


Mariam Dhayni. Problems in numerical semigroups. General Mathematics [math.GM]. Université d'Angers, 2017. English. ⟨NNT : 2017ANGE0041⟩. ⟨tel-01672101v2⟩



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