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 \(2 \times 2\) and \((n,j,k)\)-good \(3 \times 3\) 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\[M =\begin{bmatrix}a & -u & -p \\-b & v & -q \\-c & -w & r\end{bmatrix}\]corresponding to a given \((n,j)\)-good \(2 \times 2\) matrix\[K_0 =\begin{bmatrix}a_0 & -u_0 \\-b_0 & v_0\end{bmatrix}\]such that \(a \leq a_0\) and \(v \leq v_0\).