![](https://d3ilqtpdwi981i.cloudfront.net/55i_rJqfdEA-iNeOKPJOWVxLr1M=/425x550/smart/https://bepress-attached-resources.s3.amazonaws.com/uploads/1e/49/cc/1e49cc66-f229-40e3-8ea3-417d8895a998/thumbnail_82f76ca7-1275-4405-b250-4890662bd58c.jpg)
Article
Counting solutions to binomial complete intersections
JOURNAL OF COMPLEXITY
Publication Date
2007
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.
Pages
82-107
Citation Information
E Cattani and A Dickenstein. "Counting solutions to binomial complete intersections" JOURNAL OF COMPLEXITY Vol. 23 Iss. 1 (2007) Available at: http://works.bepress.com/eduardo_cattani/10/
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