On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type
ABSTRACT: Categorification of integer sequences A083329, A000295 and A049611 in the OEIS is given by using the number of sections in the Auslander-Reiten quiver of path algebras of type kΔ, where Δ is an oriented Dynkin diagram of type 6 7 An, Dn, E , E and . E8 In particular, the sequence A000295 c...
- Autores:
-
Giraldo Salazar, Hernán Alonso
Moreno Cañadas, Agustín
Bravo Ríos, Gabriel
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2017
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/40425
- Acceso en línea:
- https://hdl.handle.net/10495/40425
- Palabra clave:
- Teoría de los números
Numbers, Theory of
Álgebra
Algebra
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/2.5/co/
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On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| title |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| spellingShingle |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type Teoría de los números Numbers, Theory of Álgebra Algebra |
| title_short |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| title_full |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| title_fullStr |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| title_full_unstemmed |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| title_sort |
On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin Type |
| dc.creator.fl_str_mv |
Giraldo Salazar, Hernán Alonso Moreno Cañadas, Agustín Bravo Ríos, Gabriel |
| dc.contributor.author.none.fl_str_mv |
Giraldo Salazar, Hernán Alonso Moreno Cañadas, Agustín Bravo Ríos, Gabriel |
| dc.contributor.researchgroup.spa.fl_str_mv |
Álgebra, Teoría de Números y Aplicaciones: ERM Álgebra U de A |
| dc.subject.lemb.none.fl_str_mv |
Teoría de los números Numbers, Theory of Álgebra Algebra |
| topic |
Teoría de los números Numbers, Theory of Álgebra Algebra |
| description |
ABSTRACT: Categorification of integer sequences A083329, A000295 and A049611 in the OEIS is given by using the number of sections in the Auslander-Reiten quiver of path algebras of type kΔ, where Δ is an oriented Dynkin diagram of type 6 7 An, Dn, E , E and . E8 In particular, the sequence A000295 counts the number of Dyck paths of semilength n having exactly one long ascent. |
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2017 |
| dc.date.issued.none.fl_str_mv |
2017 |
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2024-07-05T21:17:44Z |
| dc.date.available.none.fl_str_mv |
2024-07-05T21:17:44Z |
| dc.type.spa.fl_str_mv |
Artículo de investigación |
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0972-0871 0971-4332 |
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https://hdl.handle.net/10495/40425 |
| dc.identifier.doi.none.fl_str_mv |
10.17654/MS101081631 |
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0972-0871 0971-4332 10.17654/MS101081631 |
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https://hdl.handle.net/10495/40425 |
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eng |
| language |
eng |
| dc.relation.citationendpage.spa.fl_str_mv |
1654 |
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8 |
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1631 |
| dc.relation.citationvolume.spa.fl_str_mv |
101 |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Far East Journal of Mathematical Sciences |
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http://creativecommons.org/licenses/by-nc-sa/2.5/co/ |
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24 páginas |
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| dc.publisher.spa.fl_str_mv |
Universidad de Allahabad |
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Allahabad, India |
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Universidad de Antioquia |
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Giraldo Salazar, Hernán AlonsoMoreno Cañadas, AgustínBravo Ríos, GabrielÁlgebra, Teoría de Números y Aplicaciones: ERMÁlgebra U de A2024-07-05T21:17:44Z2024-07-05T21:17:44Z20170972-08710971-4332https://hdl.handle.net/10495/4042510.17654/MS101081631ABSTRACT: Categorification of integer sequences A083329, A000295 and A049611 in the OEIS is given by using the number of sections in the Auslander-Reiten quiver of path algebras of type kΔ, where Δ is an oriented Dynkin diagram of type 6 7 An, Dn, E , E and . E8 In particular, the sequence A000295 counts the number of Dyck paths of semilength n having exactly one long ascent.Universidad de Antioquia. Vicerrectoría de investigación. Comité para el Desarrollo de la Investigación - CODICOL0017217COL008689624 páginasapplication/pdfengUniversidad de AllahabadAllahabad, Indiahttp://creativecommons.org/licenses/by-nc-sa/2.5/co/https://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2On the Number of Sections in the Auslander-Reiten Quiver of Algebras of Dynkin TypeArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTeoría de los númerosNumbers, Theory ofÁlgebraAlgebra165481631101Far East Journal of Mathematical SciencesRoR:03bp5hc83PublicationORIGINALGiraldoHernan_2017_OnNumberSections.pdfGiraldoHernan_2017_OnNumberSections.pdfArtículo de investigaciónapplication/pdf1614387https://bibliotecadigital.udea.edu.co/bitstreams/239009da-701b-4813-bff4-64cba68da241/downloadd129da65ab351f0696239adae0c74273MD51trueAnonymousREADCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051https://bibliotecadigital.udea.edu.co/bitstreams/21998675-aee3-4006-a618-2cff585c2113/downloade2060682c9c70d4d30c83c51448f4eedMD52falseAnonymousREADLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstreams/d093781a-a251-472e-91aa-c6df460b1638/download8a4605be74aa9ea9d79846c1fba20a33MD53falseAnonymousREADTEXTGiraldoHernan_2017_OnNumberSections.pdf.txtGiraldoHernan_2017_OnNumberSections.pdf.txtExtracted texttext/plain29801https://bibliotecadigital.udea.edu.co/bitstreams/159c1ea9-9f84-443c-b3e5-7f5f09758e9c/downloadce787fb2e75d9af820012abf1cd80917MD56falseAnonymousREADTHUMBNAILGiraldoHernan_2017_OnNumberSections.pdf.jpgGiraldoHernan_2017_OnNumberSections.pdf.jpgGenerated Thumbnailimage/jpeg8969https://bibliotecadigital.udea.edu.co/bitstreams/fd3a614d-92c4-4d1c-b2e0-3256eeabe1c2/downloade74321a8dd1dda1b636a0aa67293feeaMD57falseAnonymousREAD10495/40425oai:bibliotecadigital.udea.edu.co:10495/404252025-03-26 18:13:11.241http://creativecommons.org/licenses/by-nc-sa/2.5/co/open.accesshttps://bibliotecadigital.udea.edu.coRepositorio Institucional de la Universidad de Antioquiaaplicacionbibliotecadigitalbiblioteca@udea.edu.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 |