A conjectura de Wilf do ponto de vista da profundidade de um semigrupo numérico e outros invariantes
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2022-08-26
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Universidade Federal de Goiás
Resumo
In this work, it will be presented the so-called Wilf’s conjecture, which asks about a
relation between invariants of numerical semigroups. Starting with examples of known
families of numerical semigroups satisfying the conjecture, it will be shown the Eliahou’s
approach [5] that corroborates to the validity of the conjecture through tools from the
depth of a numerical semigroup. This result greatly contributes with the methods for the
conjecture and determines a new invariant to be studied in numerical semigroups: the
Eliahou number. It will be presented some basic concepts and properties about numerical
semigroups, as well as as the prerequisites for the method of Eliahou to prove that
numerical semigroups with depth q ≤ 3 satisfy the Wilf’s conjecture.
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TÔLEDO, A. C. G. A conjectura de Wilf do ponto de vista da profundidade de um semigrupo numérico e outros invariantes. 2022. 83 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.