Dense, positioned and almost-positioned numerical semigroups

Bibliographic Details
Main Author: Faria, Manuel António Silva Ramos Caldas
Publication Date: 2022
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10362/138513
Summary: The main purpose for this work is to solve the Frobenius problem for some classes of numerical semigroups and prove the Wilf’s conjecture for some other classes of numerical semigroups. First we study dense numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups, and we solve the Frobenius problem for embedding dimension three. Then we treat the positioned numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups and we prove Wilf’s conjecture. Finally we study the almost-positioned numerical semigroups, again proving Wilf’s conjecture.
id RCAP_920d5b9d31df8b938cbd7a55ff09537e
oai_identifier_str oai:run.unl.pt:10362/138513
network_acronym_str RCAP
network_name_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository_id_str https://opendoar.ac.uk/repository/7160
spelling Dense, positioned and almost-positioned numerical semigroupsNumerical semigroupsDense numerical semigroupsPositioned numerical semigroupsC-semigroupsD-semigroupsM-semigroupsDomínio/Área Científica::Ciências Naturais::MatemáticasThe main purpose for this work is to solve the Frobenius problem for some classes of numerical semigroups and prove the Wilf’s conjecture for some other classes of numerical semigroups. First we study dense numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups, and we solve the Frobenius problem for embedding dimension three. Then we treat the positioned numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups and we prove Wilf’s conjecture. Finally we study the almost-positioned numerical semigroups, again proving Wilf’s conjecture.O objectivo deste trabalho é o de obter a solução do problema de Frobenius para algumas classes de semigrupos numéricos e de provar a conjectura de Wilf para algumas outras classes de semigrupos numéricos. Primeiro estudamos os semigrupos numéricos densos, apresentando algorítmos que nos permitem obter o conjunto completo destes semigrupos e obtemos a solução do problema de Frobenius para dimensão de imersão três. De seguida tratamos os semigrupos numéricos posicionados, apresentando algorítmos que nos permitem obter o conjunto completo destes semigrupos e provamos a conjectura de Wilf. Finalmente estudamos os semigrupos numéricos quase-posicionados e mais uma vez provamos a conjectura de Wilf.Branco, ManuelRosales, JoséJesus, ManuelRUNFaria, Manuel António Silva Ramos Caldas2022-05-24T17:19:26Z2022-042022-04-01T00:00:00Zdoctoral thesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10362/138513enginfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-22T18:01:46Zoai:run.unl.pt:10362/138513Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T17:32:52.962443Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Dense, positioned and almost-positioned numerical semigroups
title Dense, positioned and almost-positioned numerical semigroups
spellingShingle Dense, positioned and almost-positioned numerical semigroups
Faria, Manuel António Silva Ramos Caldas
Numerical semigroups
Dense numerical semigroups
Positioned numerical semigroups
C-semigroups
D-semigroups
M-semigroups
Domínio/Área Científica::Ciências Naturais::Matemáticas
title_short Dense, positioned and almost-positioned numerical semigroups
title_full Dense, positioned and almost-positioned numerical semigroups
title_fullStr Dense, positioned and almost-positioned numerical semigroups
title_full_unstemmed Dense, positioned and almost-positioned numerical semigroups
title_sort Dense, positioned and almost-positioned numerical semigroups
author Faria, Manuel António Silva Ramos Caldas
author_facet Faria, Manuel António Silva Ramos Caldas
author_role author
dc.contributor.none.fl_str_mv Branco, Manuel
Rosales, José
Jesus, Manuel
RUN
dc.contributor.author.fl_str_mv Faria, Manuel António Silva Ramos Caldas
dc.subject.por.fl_str_mv Numerical semigroups
Dense numerical semigroups
Positioned numerical semigroups
C-semigroups
D-semigroups
M-semigroups
Domínio/Área Científica::Ciências Naturais::Matemáticas
topic Numerical semigroups
Dense numerical semigroups
Positioned numerical semigroups
C-semigroups
D-semigroups
M-semigroups
Domínio/Área Científica::Ciências Naturais::Matemáticas
description The main purpose for this work is to solve the Frobenius problem for some classes of numerical semigroups and prove the Wilf’s conjecture for some other classes of numerical semigroups. First we study dense numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups, and we solve the Frobenius problem for embedding dimension three. Then we treat the positioned numerical semigroups, presenting algorithms that allow us to obtain the whole set of these semigroups and we prove Wilf’s conjecture. Finally we study the almost-positioned numerical semigroups, again proving Wilf’s conjecture.
publishDate 2022
dc.date.none.fl_str_mv 2022-05-24T17:19:26Z
2022-04
2022-04-01T00:00:00Z
dc.type.driver.fl_str_mv doctoral thesis
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/138513
url http://hdl.handle.net/10362/138513
dc.language.iso.fl_str_mv eng
language eng
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.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
_version_ 1833596775541243904

Similar Items