Counting Solutions to Binomial Complete Intersections
Commutative Algebra
2007-05-23 v2 Computational Complexity
Combinatorics
Abstract
We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.
Cite
@article{arxiv.math/0510520,
title = {Counting Solutions to Binomial Complete Intersections},
author = {Eduardo Cattani and Alicia Dickenstein},
journal= {arXiv preprint arXiv:math/0510520},
year = {2007}
}
Comments
Several minor improvements. Final version to appear in the J. of Complexity