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Fibonacci-like behavior of the number of numerical semigroups of a given genus

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Abstract

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same range.

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References

  1. Apéry, R.: Sur les branches superlinéaires des courbes algébriques. C.R. Acad. Sci. Paris 222, 1198–1200 (1946)

    MATH  MathSciNet  Google Scholar 

  2. Dobbs, D.E., Matthews, G.L.: On a question of Wilf concerning numerical semigroups. Int. J. Commut. 3(2) (2003)

  3. Fröberg, R., Gottlieb, C., Häggkvist, R.: On numerical semigroups. Semigroup Forum 35(1), 63–83 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Madero-Craven, M., Herzinger, K.: Apery sets of numerical semigroups. Commun. Algebra 33(10), 3831–3838 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Rosales, J.C., García-Sánchez, P.A., García-García, J.I., Branco, M.B.: Systems of inequalities and numerical semigroups. J. Lond. Math. Soc. (2) 65(3), 611–623 (2002)

    Article  MATH  Google Scholar 

  6. Rosales, J.C., García-Sánchez, P.A., García-García, J.I., Branco, M.B.: Numerical semigroups with a monotonic Apéry set. Czechoslov. Math. J. 55(130)(3), 755–772 (2005)

    Article  MATH  Google Scholar 

  7. Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences. Published electronically at www.research.att.com/~njas/sequences/ (A007323) (2007)

  8. Wilf, H.S.: A circle-of-lights algorithm for the “money-changing problem”. Am. Math. Mon. 85(7), 562–565 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Catalonia, Spain

    Maria Bras-Amorós

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  1. Maria Bras-Amorós
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Correspondence to Maria Bras-Amorós.

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Communicated by Jorge Almeida

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Bras-Amorós, M. Fibonacci-like behavior of the number of numerical semigroups of a given genus. Semigroup Forum 76, 379–384 (2008). https://doi.org/10.1007/s00233-007-9014-8

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  • DOI: https://doi.org/10.1007/s00233-007-9014-8

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