Hyperplane arrangements between Shi and Ish

Detalhes bibliográficos
Autor(a) principal: Duarte, Rui
Data de Publicação: 2018
Outros Autores: Guedes de Oliveira, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/24131
Resumo: We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the complement of the union of the hyperplanes -- which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.
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spelling Hyperplane arrangements between Shi and IshHyperplane arrangementsShi arrangementIsh arrangementPak-Stanley labellingParking functionsWe introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the complement of the union of the hyperplanes -- which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.Elsevier2020-12-01T00:00:00Z2018-07-01T00:00:00Z2018-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/24131eng1571-065310.1016/j.endm.2018.06.046Duarte, RuiGuedes de Oliveira, Antónioinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:47:25Zoai:ria.ua.pt:10773/24131Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:57:54.414052Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Hyperplane arrangements between Shi and Ish
title Hyperplane arrangements between Shi and Ish
spellingShingle Hyperplane arrangements between Shi and Ish
Duarte, Rui
Hyperplane arrangements
Shi arrangement
Ish arrangement
Pak-Stanley labelling
Parking functions
title_short Hyperplane arrangements between Shi and Ish
title_full Hyperplane arrangements between Shi and Ish
title_fullStr Hyperplane arrangements between Shi and Ish
title_full_unstemmed Hyperplane arrangements between Shi and Ish
title_sort Hyperplane arrangements between Shi and Ish
author Duarte, Rui
author_facet Duarte, Rui
Guedes de Oliveira, António
author_role author
author2 Guedes de Oliveira, António
author2_role author
dc.contributor.author.fl_str_mv Duarte, Rui
Guedes de Oliveira, António
dc.subject.por.fl_str_mv Hyperplane arrangements
Shi arrangement
Ish arrangement
Pak-Stanley labelling
Parking functions
topic Hyperplane arrangements
Shi arrangement
Ish arrangement
Pak-Stanley labelling
Parking functions
description We introduce a new family of hyperplane arrangements in dimension n≥3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of this family have the same number of regions -- the connected components of the complement of the union of the hyperplanes -- which can be bijectively labeled with the Pak-Stanley labelling. In addition, we characterise the Pak-Stanley labels of the regions of this family of hyperplane arrangements.
publishDate 2018
dc.date.none.fl_str_mv 2018-07-01T00:00:00Z
2018-07
2020-12-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/24131
url http://hdl.handle.net/10773/24131
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1571-0653
10.1016/j.endm.2018.06.046
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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