Counting solutions to binomial complete intersections
This is the pre-published version harvested from ArXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WHX-4K7FJCX-1&_user=1516330&_coverDate=02%2F28%2F2007&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1662372887&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=fe0f34aeb86639c32ede298f34158305&searchtype=a
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.
E Cattani and A Dickenstein. "Counting solutions to binomial complete intersections" Journal of Complexity 23.1 (2007): 82-107.
Available at: http://works.bepress.com/eduardo_cattani/10