Counting Solutions to Binomial Complete Intersections
<|reference_start|>Counting Solutions to Binomial Complete Intersections: 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.<|reference_end|>
@article{cattani2005counting,
    title={Counting Solutions to Binomial Complete Intersections},
    author={Eduardo Cattani and Alicia Dickenstein},
    journal={arXiv preprint arXiv:math/0510520},
    year={2005},
    archivePrefix={arXiv},
    eprint={math/0510520},
    primaryClass={math.AC cs.CC math.CO}
}