Counting solutions to binomial complete intersections

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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 n...

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Autores principales:	Cattani, E., Dickenstein, A.
Formato:	Artículo publishedVersion
Publicado:	2007
Materias:	# P-complete Binomial ideal Complete intersection Computational methods Polynomials Problem solving Vectors Binomials Polynomial time Algebra
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v23_n1_p82_Cattani_oai
Aporte de:	Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires

id	I28-R145-paper_0885064X_v23_n1_p82_Cattani_oai
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spelling	I28-R145-paper_0885064X_v23_n1_p82_Cattani_oai2020-10-19 Cattani, E. Dickenstein, A. 2007 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. © 2006 Elsevier Inc. All rights reserved. Fil:Cattani, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Complexity 2007;23(1):82-107 # P-complete Binomial ideal Complete intersection Computational methods Polynomials Problem solving Vectors Binomials Complete intersection Polynomial time Algebra Counting solutions to binomial complete intersections info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v23_n1_p82_Cattani_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	# P-complete Binomial ideal Complete intersection Computational methods Polynomials Problem solving Vectors Binomials Complete intersection Polynomial time Algebra
spellingShingle	# P-complete Binomial ideal Complete intersection Computational methods Polynomials Problem solving Vectors Binomials Complete intersection Polynomial time Algebra Cattani, E. Dickenstein, A. Counting solutions to binomial complete intersections
topic_facet	# P-complete Binomial ideal Complete intersection Computational methods Polynomials Problem solving Vectors Binomials Complete intersection Polynomial time Algebra
description	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. © 2006 Elsevier Inc. All rights reserved.
format	Artículo Artículo publishedVersion
author	Cattani, E. Dickenstein, A.
author_facet	Cattani, E. Dickenstein, A.
author_sort	Cattani, E.
title	Counting solutions to binomial complete intersections
title_short	Counting solutions to binomial complete intersections
title_full	Counting solutions to binomial complete intersections
title_fullStr	Counting solutions to binomial complete intersections
title_full_unstemmed	Counting solutions to binomial complete intersections
title_sort	counting solutions to binomial complete intersections
publishDate	2007
url	http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_0885064X_v23_n1_p82_Cattani_oai
work_keys_str_mv	AT cattanie countingsolutionstobinomialcompleteintersections AT dickensteina countingsolutionstobinomialcompleteintersections
_version_	1766026714003013632

Counting solutions to binomial complete intersections

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