Counting numerical semigroups by genus and even gaps |
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Authors: | Matheus Bernardini Fernando Torres |
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Institution: | 1. IMECC/UNICAMP, R. Sérgio Buarque de Holanda 651, Cidade Universitária “Zeferino Vaz”, 13083-859, Campinas, SP, Brazil;2. Instituto Federal de São Paulo, Av. Comendador Aladino Selmi, s/no Prédio 4 CTI Renato Archer, 13069-901, Campinas, SP, Brazil |
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Abstract: | Let be the number of numerical semigroups of genus . We present an approach to compute by using even gaps, and the question: Is it true that ? is investigated. Let be the number of numerical semigroups of genus whose number of even gaps equals . We show that for and for ; thus the question above is true provided that for . We also show that coincides with , the number introduced by Bras-Amorós (2012) in connection with semigroup-closed sets. Finally, the stronger possibility arises being the golden number. |
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Keywords: | Numerical semigroup Even gap Genus Correspondence to: IMECC/UNICAMP R Sérgio Buarque de Holanda 651 Cidade Universitária “Zeferino Vaz” 13083-859 Campinas SP Brazil |
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