AN ALGORITHM FOR A CLASS OF (n,j,k)- GOOD MATRICES RELATED TO NUMERICAL SEMIGROUPS WITH EMBEDDING DIMENSION 4 - Bajrami, Merita; Dimovski, Dončo; Angjelkoska, Violeta (Matematichki Bilten, 2023)
In this paper, first we recall the definitions of \((n,j)\)-good \(2 × 2\) and \((n,j,k)\)-good \(3 × 3\) integer matrices, connected to numerical semigroups of embedding dimension 3 and 4, respectively. Then, for given natural numbers \(n\), \(j\) and \(k\) where \(1 < j, k < n\) and \(k eq j\), we present an algorithm for obtaining all the \((n,j,k)\)-good matrices \[ M = bmatrix a & -u & -p -b & v & -q -c & -w & r bmatrix \] corresponding to a given \((n,j)\)-good \(2 × 2\) matrix \[ K_0 = bmatrix a_0 & -u_0 -b_0 & v_0 bmatrix \] such that \(a ≤ a_0\) and \(v ≤ v_0\).