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
- 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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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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1846784876604293120 |
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12.982451 |