Algebraic Unimodular Counting

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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 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.
21 pages

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Combinatorics, Commutative Algebra, Algebraic Geometry, 05A15; 13P10; 52B20; 68W30

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http://salesiana.dossiersoluciones.com/handle/123456789/61397

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0104286
 http://arxiv.org/abs/math/0104286

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arXiv