Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples
Leonid G. Fel
TL;DR
This paper investigates symmetric numerical semigroups generated by Fibonacci and Lucas triples, establishing conditions for symmetry and computing key algebraic invariants like Hilbert series, Frobenius numbers, and genus.
Contribution
It provides necessary and sufficient conditions for symmetry and explicit calculations of algebraic invariants for these semigroups, based on divisibility properties.
Findings
Conditions for symmetry of the semigroups are established.
Explicit formulas for Frobenius numbers and genus are derived.
Hilbert generating series are computed for the semigroups.
Abstract
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.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics