Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples

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The symmetric numerical semigroups S(F_a,F_b,F_c) and S(L_k,L_m,L_n) generated by three Fibonacci (F_a,F_b,F_c) and Lucas (L_k,L_m,L_n) numbers are considered. Based on divisibility properties of the Fibonacci and Lucas numbers we establish necessary and sufficient conditions for both semigroups to be symmetric and calculate their Hilbert generating series, Frobenius numbers and genera.
10 pages

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Number Theory, Commutative Algebra, 20M14, 11N37

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http://salesiana.dossiersoluciones.com/handle/123456789/156662

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.1606
 http://arxiv.org/abs/0803.1606

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arXiv