Classification of thin regular map representations of hypermaps
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/39692 |
Resumo: | There are two well known maps representations of hypermaps, namely the Walsh and the Vince map representations, being dual of each other. They correspond to normal sub groups of index two of a free product Γ = (C2 × C2) ∗ C2 which decompose as “elemen tary” free product C2 ∗ C2 ∗ C2. However Γ has three normal subgroups that decompose as “elementary” free product C2 ∗ C2 ∗ C2, the third of these sbgroups giving the less known petrie-path map representation. By relaxing the “elementary” free product condition to free product of rank 3, and under the extra condition “words of smaller length” on the genera tors, we prove that the number of map representations of hypermaps increases to 15 (up to a restrictedly dual), all of which described in this paper. |
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Classification of thin regular map representations of hypermapsMap representationHypermapsMapsRegularityRestricted regularityOrientably regularThere are two well known maps representations of hypermaps, namely the Walsh and the Vince map representations, being dual of each other. They correspond to normal sub groups of index two of a free product Γ = (C2 × C2) ∗ C2 which decompose as “elemen tary” free product C2 ∗ C2 ∗ C2. However Γ has three normal subgroups that decompose as “elementary” free product C2 ∗ C2 ∗ C2, the third of these sbgroups giving the less known petrie-path map representation. By relaxing the “elementary” free product condition to free product of rank 3, and under the extra condition “words of smaller length” on the genera tors, we prove that the number of map representations of hypermaps increases to 15 (up to a restrictedly dual), all of which described in this paper.University of Primorska2023-11-15T14:36:35Z2023-01-13T00:00:00Z2023-01-13info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/39692eng1855-396610.26493/1855-3974.2503.f17D’Azevedo, Antonio BredaCatalano, Domenico A.info: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:RCAAP2024-02-22T12:17:43Zoai:ria.ua.pt:10773/39692Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:09:52.471502Repositório 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 |
Classification of thin regular map representations of hypermaps |
title |
Classification of thin regular map representations of hypermaps |
spellingShingle |
Classification of thin regular map representations of hypermaps D’Azevedo, Antonio Breda Map representation Hypermaps Maps Regularity Restricted regularity Orientably regular |
title_short |
Classification of thin regular map representations of hypermaps |
title_full |
Classification of thin regular map representations of hypermaps |
title_fullStr |
Classification of thin regular map representations of hypermaps |
title_full_unstemmed |
Classification of thin regular map representations of hypermaps |
title_sort |
Classification of thin regular map representations of hypermaps |
author |
D’Azevedo, Antonio Breda |
author_facet |
D’Azevedo, Antonio Breda Catalano, Domenico A. |
author_role |
author |
author2 |
Catalano, Domenico A. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
D’Azevedo, Antonio Breda Catalano, Domenico A. |
dc.subject.por.fl_str_mv |
Map representation Hypermaps Maps Regularity Restricted regularity Orientably regular |
topic |
Map representation Hypermaps Maps Regularity Restricted regularity Orientably regular |
description |
There are two well known maps representations of hypermaps, namely the Walsh and the Vince map representations, being dual of each other. They correspond to normal sub groups of index two of a free product Γ = (C2 × C2) ∗ C2 which decompose as “elemen tary” free product C2 ∗ C2 ∗ C2. However Γ has three normal subgroups that decompose as “elementary” free product C2 ∗ C2 ∗ C2, the third of these sbgroups giving the less known petrie-path map representation. By relaxing the “elementary” free product condition to free product of rank 3, and under the extra condition “words of smaller length” on the genera tors, we prove that the number of map representations of hypermaps increases to 15 (up to a restrictedly dual), all of which described in this paper. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-11-15T14:36:35Z 2023-01-13T00:00:00Z 2023-01-13 |
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/10773/39692 |
url |
http://hdl.handle.net/10773/39692 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1855-3966 10.26493/1855-3974.2503.f17 |
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 |
University of Primorska |
publisher.none.fl_str_mv |
University of Primorska |
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) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137749576450048 |