On Numerical Experiments with Symmetric Semigroups Generated by Three Elements and Their Generalization
| dc.creator | Fel, Leonid G. | |
| dc.date | 2009-03-22 | |
| dc.date.accessioned | 2026-07-07T12:55:36Z | |
| dc.date.available | 2026-07-07T12:55:36Z | |
| dc.description | We give a simple explanation of numerical experiments of V. Arnold with two sequences of symmetric numerical semigroups, S(4,6+4k,87-4k) and S(9,3+9k,85-9k) generated by three elements. We present a generalization of these sequences by numerical semigroups S(r_1^2,r_1r_2+r_1^2k,r_3-r_1^2k), k\in{\mathbb Z}, r_1,r_2,r_3\in{\mathbb Z}^+, r_1\geq 2 and \gcd(r_1,r_2)=\gcd(r_1,r_3)=1, and calculate their universal Frobenius number Phi(r_1,r_2,r_3) for the wide range of k providing semigroups be symmetric. We show that this kind of semigroups admit also nonsymmetric representatives. We describe the reduction of the minimal generating sets of these semigroups up to {r_1^2,r_3-r_1^2k} for sporadic values of k and find these values by solving the quadratic Diophantine equation. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0903.3756 | |
| dc.identifier | http://arxiv.org/abs/0903.3756 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224304 | |
| dc.subject | Number Theory | |
| dc.subject | 20M14 | |
| dc.title | On Numerical Experiments with Symmetric Semigroups Generated by Three Elements and Their Generalization | |
| dc.type | text |