Algebraic unimodular counting

Algebraic unimodular counting

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Article ID: iaor20041798
Country: Germany
Volume: 96
Issue: 2
Start Page Number: 183
End Page Number: 203
Publication Date: Jan 2003
Journal: Mathematical Programming
Authors: ,
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.

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