Counting solutions to binomial complete intersections

Autores
Cattani, E.; Dickenstein, A.
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fuente
J. Complexity 2007;23(1):82-107
Materia
# P-complete
Binomial ideal
Complete intersection
Computational methods
Polynomials
Problem solving
Vectors
Binomials
Complete intersection
Polynomial time
Algebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_0885064X_v23_n1_p82_Cattani
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network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Counting solutions to binomial complete intersectionsCattani, E.Dickenstein, A.# P-completeBinomial idealComplete intersectionComputational methodsPolynomialsProblem solvingVectorsBinomialsComplete intersectionPolynomial timeAlgebraWe 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.2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_CattaniJ. Complexity 2007;23(1):82-107reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-23T11:18:16Zpaperaa:paper_0885064X_v23_n1_p82_CattaniInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-23 11:18:17.281Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Counting solutions to binomial complete intersections
title Counting solutions to binomial complete intersections
spellingShingle Counting solutions to binomial complete intersections
Cattani, E.
# P-complete
Binomial ideal
Complete intersection
Computational methods
Polynomials
Problem solving
Vectors
Binomials
Complete intersection
Polynomial time
Algebra
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
dc.creator.none.fl_str_mv Cattani, E.
Dickenstein, A.
author Cattani, E.
author_facet Cattani, E.
Dickenstein, A.
author_role author
author2 Dickenstein, A.
author2_role author
dc.subject.none.fl_str_mv # P-complete
Binomial ideal
Complete intersection
Computational methods
Polynomials
Problem solving
Vectors
Binomials
Complete intersection
Polynomial time
Algebra
topic # P-complete
Binomial ideal
Complete intersection
Computational methods
Polynomials
Problem solving
Vectors
Binomials
Complete intersection
Polynomial time
Algebra
dc.description.none.fl_txt_mv 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.
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.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani
url http://hdl.handle.net/20.500.12110/paper_0885064X_v23_n1_p82_Cattani
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv J. Complexity 2007;23(1):82-107
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.982451

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