Polyhedral Omega (+ applications)

par Prof. Zafeirakis Zafeirakopoulos

mardi 23 mai 2023, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux, Bât Braconnier (ICJ, Université Lyon 1)

Polyhedral Omega is an algorithm for solving linear Diophantine systems, 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 Omega combines 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 Brion decomposition and Barvinok’s short rational function representations. This synthesis of ideas makes Polyhedral Omega by far the simplest algorithm for solving linear Diophantine systems available to date.
After presenting the algorithm, we will see some applications and generalizations.