NUMERICAL SEMIGROUPS FROM RATIONAL MATRICES IV: COMPUTATION OF THE MATRICIAL DIMENSIONS OF NUMERICAL SEMIGROUPS WITH SMALL FROBENIUS NUMBER OR GENUS

Abstract We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimensions of numerical semigroups. We compute the matricial dimension of every numerical semigroup with Frobenius number at most $10$ or genus at most $6$ . Many of these evaluations are beyond the scope of previous techniques.