@article{Kohl2016SemigroupsA,
title={Semigroups – A computational approach},
author={F. Kohl and Y. Li and J. Rauh and R. Yoshida},
journal={arXiv: Combinatorics},
year={2016},
pages={155-170}
}

The question whether there exists an integral solution to the system of linear equations with non-negative constraints, $A\x = \b, \, \x \ge 0$, where $A \in \Z^{m\times n}$ and ${\mathbf b} \in \Z^m$, finds its applications in many areas, such as operation research, number theory and statistics. In order to solve this problem, we have to understand the semigroup generated by the columns of the matrix $A$ and the structure of the "holes" which are the difference between the semigroup generated… CONTINUE READING