- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 1
- Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number
Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number
Authors : José Carlos Rosales, Manuel B. Branco, M. C. Faria
Pages : 218-227
Doi:10.15672/hujms.897234
View : 10 | Download : 3
Publication Date : 2022-02-14
Article Type : Research
Abstract :A $C$-semigroup (respectively a $D$-semigroup) is a positioned numerical semigroup $S$ such that $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-1}{2}$ (respectively $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-2}{2}$). In this paper we study these semigroups giving formulas for the Frobenius number, pseudo-Frobenius number, and type. Furthermore, we give algorithms for computing the whole set of $C$-semigroups and $D$-semigroups.Keywords : numerical semigroups, positioned numerical semigroups, $C$-semigroups, $D$-semigroups tree, Frobenius number, multiplicity and gender