English

Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples

Number Theory 2008-03-12 v1 Commutative Algebra

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.

Keywords

Cite

@article{arxiv.0803.1606,
  title  = {Symmetric Numerical Semigroups Generated by Fibonacci and Lucas Triples},
  author = {Leonid G. Fel},
  journal= {arXiv preprint arXiv:0803.1606},
  year   = {2008}
}

Comments

10 pages

R2 v1 2026-06-21T10:20:33.500Z