The Frobenius problem for numerical semigroups (Q640865)

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.