Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number

Authors : José Carlos ROSALES, Manuel B. BRANCO, M. C. FARİA

Pages : 218-227

Doi:10.15672/hujms.897234

View : 21 | Download : 4

Publication Date : 2022-02-14

Article Type : Research Paper

Abstract :A $C$-semigroup insert ignore into journalissuearticles values(respectively a $D$-semigroup); is a positioned numerical semigroup $S$ such that $\rm{g}insert ignore into journalissuearticles values(S);=\frac{\rm{F}insert ignore into journalissuearticles values(S);+\rm{m}insert ignore into journalissuearticles values(S);-1}{2}$ insert ignore into journalissuearticles values(respectively $\rm{g}insert ignore into journalissuearticles values(S);=\frac{\rm{F}insert ignore into journalissuearticles values(S);+\rm{m}insert ignore into journalissuearticles values(S);-2}{2}$);. 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