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Algebraic unimodular counting

By Jesús A. De Loera and Bernd Sturmfels

Abstract

We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gröbner bases, and rational generating functions as in Barvinok's algorithm. We report polyhedral and computational results for two special cases: counting contingency tables and Kostant's partition function

Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.3526
Provided by: CiteSeerX
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