Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems

@article{Breuer2015PolyhedralOA,
  title={Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems},
  author={Felix Breuer and Zafeirakis Zafeirakopoulos},
  journal={Annals of Combinatorics},
  year={2015},
  volume={21},
  pages={211-280}
}
Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and inequalities. Polyhedral Omegacombines methods from partition analysis with methods from polyhedral geometry. In particular, we combine MacMahon’s iterative approach based on the Omega operator and explicit formulas for its evaluation with geometric tools such as… 
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