Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
Abstract
The symmetric numerical semigroups S(Fa,Fb,Fc) and S(Lk,Lm,Ln) generated by three Fibonacci (Fa,Fb,Fc) and Lucas (Lk,Lm,Ln) 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.
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