Algebraic Unimodular Counting
Combinatorics
2007-05-23 v1 Commutative Algebra
Algebraic Geometry
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.
Cite
@article{arxiv.math/0104286,
title = {Algebraic Unimodular Counting},
author = {Jesus A. De Loera and Bernd Sturmfels},
journal= {arXiv preprint arXiv:math/0104286},
year = {2007}
}
Comments
21 pages