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Algebraic Unimodular Counting
Published Web Location
https://arxiv.org/pdf/math/0104286.pdfNo data is associated with this publication.
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 Gr\"obner 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.