Journal
MATHEMATICAL PROGRAMMING
Volume 96, Issue 2, Pages 183-203Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-003-0383-9
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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 Grobner 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.
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