The Frobenius problem for numerical semigroups
The paper provides a new method for computing the Frobenius number. The main idea of the method is the following. With the use of special projection any semigroup containing \(\langle n_1,n_2 \rangle\) can be characterized as a subset of incomparable elements of the set \[ B(n_1,n_2)=\{(a,b): 0<a<n_2, 0<b<n_1,\; n_1n_2-an_1-bn_2\geq0\}. \] Using this characterization the algorithm for computing of the Frobenius number of a numerical semigroup is presented. It should be mentioned that the method for the case of three dimensional numerical semigroup is formulated in terms of its minimal system of generators.
scientific article; zbMATH DE number 5960854