Department of Mathematics
Polyhedral Omega: Solving linear Diophantine systems
Abstract: 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 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.
Date: Thursday, November 24, 2016
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the talk. All are most cordially invited.