Classification of the regular oriented hypermaps with a prime number of hyperfaces
Autor(a) principal: | |
---|---|
Data de Publicação: | 2016 |
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/10773/16676 |
Resumo: | Regular oriented hypermaps are triples (G; a; b) consisting of a nite 2-generated group G and a pair a, b of generators of G, where the left cosets of ⟨a⟩, ⟨b⟩ and ⟨ab⟩ describe respectively the hyperfaces, hypervertices and hyperedges. They generalise regular oriented maps (triples with ab of order 2) and describe cellular embeddings of regular hypergraphs on orientable surfaces. In [5] we have classi ed the regular oriented hypermaps with prime number hyperfaces and with no non-trivial regular proper quotients with the same number of hyperfaces (i.e. primer hypermaps with prime number of hyperfaces), which generalises the classi cation of regular oriented maps with prime number of faces and underlying simple graph [13]. Now we classify the regular oriented hypermaps with a prime number of hyperfaces. As a result of this classi cation, we conclude that the regular oriented hypermaps with prime p hyperfaces have metacyclic automorphism groups and the chiral ones have cyclic chirality groups; of these the \canonical metacyclic" (i.e. those for which ⟨a⟩ is normal in G) have chirality index a divisor of n (the hyperface valency) and the non \canonical metacyclic" have chirality index p. We end the paper by counting, for each positive integer n and each prime p, the number of regular oriented hypermaps with p hyperfaces of valency n. |
id |
RCAP_073dba24824e466cdc8dbe2e326bb381 |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/16676 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Classification of the regular oriented hypermaps with a prime number of hyperfacesHypermapsMapsHypergraphsRegularityOrientably regularChiralityRegular oriented hypermaps are triples (G; a; b) consisting of a nite 2-generated group G and a pair a, b of generators of G, where the left cosets of ⟨a⟩, ⟨b⟩ and ⟨ab⟩ describe respectively the hyperfaces, hypervertices and hyperedges. They generalise regular oriented maps (triples with ab of order 2) and describe cellular embeddings of regular hypergraphs on orientable surfaces. In [5] we have classi ed the regular oriented hypermaps with prime number hyperfaces and with no non-trivial regular proper quotients with the same number of hyperfaces (i.e. primer hypermaps with prime number of hyperfaces), which generalises the classi cation of regular oriented maps with prime number of faces and underlying simple graph [13]. Now we classify the regular oriented hypermaps with a prime number of hyperfaces. As a result of this classi cation, we conclude that the regular oriented hypermaps with prime p hyperfaces have metacyclic automorphism groups and the chiral ones have cyclic chirality groups; of these the \canonical metacyclic" (i.e. those for which ⟨a⟩ is normal in G) have chirality index a divisor of n (the hyperface valency) and the non \canonical metacyclic" have chirality index p. We end the paper by counting, for each positive integer n and each prime p, the number of regular oriented hypermaps with p hyperfaces of valency n.DMFA Slovenije2017-01-20T12:33:24Z2016-01-01T00:00:00Z2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16676eng1855-3966Breda d'Azevedo, AntónioFernandes, Maria Elisainfo: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:RCAAP2024-02-22T11:31:15Zoai:ria.ua.pt:10773/16676Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:47.610710Repositório 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 the regular oriented hypermaps with a prime number of hyperfaces |
title |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
spellingShingle |
Classification of the regular oriented hypermaps with a prime number of hyperfaces Breda d'Azevedo, António Hypermaps Maps Hypergraphs Regularity Orientably regular Chirality |
title_short |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
title_full |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
title_fullStr |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
title_full_unstemmed |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
title_sort |
Classification of the regular oriented hypermaps with a prime number of hyperfaces |
author |
Breda d'Azevedo, António |
author_facet |
Breda d'Azevedo, António Fernandes, Maria Elisa |
author_role |
author |
author2 |
Fernandes, Maria Elisa |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Breda d'Azevedo, António Fernandes, Maria Elisa |
dc.subject.por.fl_str_mv |
Hypermaps Maps Hypergraphs Regularity Orientably regular Chirality |
topic |
Hypermaps Maps Hypergraphs Regularity Orientably regular Chirality |
description |
Regular oriented hypermaps are triples (G; a; b) consisting of a nite 2-generated group G and a pair a, b of generators of G, where the left cosets of ⟨a⟩, ⟨b⟩ and ⟨ab⟩ describe respectively the hyperfaces, hypervertices and hyperedges. They generalise regular oriented maps (triples with ab of order 2) and describe cellular embeddings of regular hypergraphs on orientable surfaces. In [5] we have classi ed the regular oriented hypermaps with prime number hyperfaces and with no non-trivial regular proper quotients with the same number of hyperfaces (i.e. primer hypermaps with prime number of hyperfaces), which generalises the classi cation of regular oriented maps with prime number of faces and underlying simple graph [13]. Now we classify the regular oriented hypermaps with a prime number of hyperfaces. As a result of this classi cation, we conclude that the regular oriented hypermaps with prime p hyperfaces have metacyclic automorphism groups and the chiral ones have cyclic chirality groups; of these the \canonical metacyclic" (i.e. those for which ⟨a⟩ is normal in G) have chirality index a divisor of n (the hyperface valency) and the non \canonical metacyclic" have chirality index p. We end the paper by counting, for each positive integer n and each prime p, the number of regular oriented hypermaps with p hyperfaces of valency n. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-01-01T00:00:00Z 2016 2017-01-20T12:33:24Z |
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/10773/16676 |
url |
http://hdl.handle.net/10773/16676 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1855-3966 |
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 |
DMFA Slovenije |
publisher.none.fl_str_mv |
DMFA Slovenije |
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 |
|
_version_ |
1799137567784828928 |