Characterization of tropical hemispaces by (P,R)-decompositions

Autores
Katz, Ricardo David; Nitica, Viorel; Sergeev, Sergei
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.
Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro de Estudios Fotosintéticos y Bioquímicos (i); Argentina
Fil: Nitica, Viorel. West Chester University; Rumania
Fil: Sergeev, Sergei. University of Birmingham. School of Mathematics; Reino Unido
Materia
TROPICAL CONVEXITY
ABSTRACT CONVEXITY
MAX-PLUS ALGEBRA
HEMISPACE
SEMISPACE
RANK-ONE MATRIX
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/4813
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/4813
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network_name_str CONICET Digital (CONICET)
spelling Characterization of tropical hemispaces by (P,R)-decompositionsKatz, Ricardo DavidNitica, ViorelSergeev, SergeiTROPICAL CONVEXITYABSTRACT CONVEXITYMAX-PLUS ALGEBRAHEMISPACESEMISPACERANK-ONE MATRIXhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro de Estudios Fotosintéticos y Bioquímicos (i); ArgentinaFil: Nitica, Viorel. West Chester University; RumaniaFil: Sergeev, Sergei. University of Birmingham. School of Mathematics; Reino UnidoElsevier2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/4813Katz, Ricardo David; Nitica, Viorel; Sergeev, Sergei; Characterization of tropical hemispaces by (P,R)-decompositions; Elsevier; Linear Algebra and its Applications; 440; 1; 1-2014; 131-1630024-3795enginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379513006630info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.10.029info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:53:51Zoai:ri.conicet.gov.ar:11336/4813instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:53:51.682CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Characterization of tropical hemispaces by (P,R)-decompositions
title Characterization of tropical hemispaces by (P,R)-decompositions
spellingShingle Characterization of tropical hemispaces by (P,R)-decompositions
Katz, Ricardo David
TROPICAL CONVEXITY
ABSTRACT CONVEXITY
MAX-PLUS ALGEBRA
HEMISPACE
SEMISPACE
RANK-ONE MATRIX
title_short Characterization of tropical hemispaces by (P,R)-decompositions
title_full Characterization of tropical hemispaces by (P,R)-decompositions
title_fullStr Characterization of tropical hemispaces by (P,R)-decompositions
title_full_unstemmed Characterization of tropical hemispaces by (P,R)-decompositions
title_sort Characterization of tropical hemispaces by (P,R)-decompositions
dc.creator.none.fl_str_mv Katz, Ricardo David
Nitica, Viorel
Sergeev, Sergei
author Katz, Ricardo David
author_facet Katz, Ricardo David
Nitica, Viorel
Sergeev, Sergei
author_role author
author2 Nitica, Viorel
Sergeev, Sergei
author2_role author
author
dc.subject.none.fl_str_mv TROPICAL CONVEXITY
ABSTRACT CONVEXITY
MAX-PLUS ALGEBRA
HEMISPACE
SEMISPACE
RANK-ONE MATRIX
topic TROPICAL CONVEXITY
ABSTRACT CONVEXITY
MAX-PLUS ALGEBRA
HEMISPACE
SEMISPACE
RANK-ONE MATRIX
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.
Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Centro de Estudios Fotosintéticos y Bioquímicos (i); Argentina
Fil: Nitica, Viorel. West Chester University; Rumania
Fil: Sergeev, Sergei. University of Birmingham. School of Mathematics; Reino Unido
description We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of (P,R)-decomposition. This yields (to our knowledge) a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays. We characterize tropical hemispaces as tropically convex sets that admit a (P,R)-decomposition of certain kind. In this characterization, with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield, satisfying an extended rank-one condition. Our proof techniques are based on homogenization (lifting a convex set to a cone), and the relation between tropical hemispaces and semispaces.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/4813
Katz, Ricardo David; Nitica, Viorel; Sergeev, Sergei; Characterization of tropical hemispaces by (P,R)-decompositions; Elsevier; Linear Algebra and its Applications; 440; 1; 1-2014; 131-163
0024-3795
url http://hdl.handle.net/11336/4813
identifier_str_mv Katz, Ricardo David; Nitica, Viorel; Sergeev, Sergei; Characterization of tropical hemispaces by (P,R)-decompositions; Elsevier; Linear Algebra and its Applications; 440; 1; 1-2014; 131-163
0024-3795
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0024379513006630
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.10.029
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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