Investigation of the gluing of the Arf numerical semigroup with RF-matrices

In this study, the concept of gluing of numerical semigroups is specialized and the gluing of Arf numerical semigroups is investigated. The structures of numerical semigroups formed by gluing Arf numerical semigroups are analyzed and presented via theorems. In addition, the RF-matrix of Arf numerical semigroups is calculated and the RF-matrix of two glued Arf numerical semigroups is found. Finally,the methods for finding the generator sets of the ideals obtained with RF-matrices are given and the studies are supported with numerical examples.