The number of s-separated k-sets in various circles

Autores
Estrugo, Emiliano Juan José; Pastine, Adrián Gabriel
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This article studies the number of ways of selecting k objects arranged in p circles of sizes n0,...,np−1 such that no two selected ones have less than s objects between them. If ni ≥ sk + 1 for all 0 ≤ i ≤ p − 1, this number is shown to be n0+...+np−2 k n0+...+np−2−sk−1 k−1 . A combinatorial proof of this claim is provided, and two convolution formulas due to Rothe are obtained as corollaries.
Fil: Estrugo, Emiliano Juan José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Pastine, Adrián Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Materia
S-Separation
N-Circle
K-Stras in Graphs
K-Sets
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/150796
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/150796
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The number of s-separated k-sets in various circlesEstrugo, Emiliano Juan JoséPastine, Adrián GabrielS-SeparationN-CircleK-Stras in GraphsK-Setshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This article studies the number of ways of selecting k objects arranged in p circles of sizes n0,...,np−1 such that no two selected ones have less than s objects between them. If ni ≥ sk + 1 for all 0 ≤ i ≤ p − 1, this number is shown to be n0+...+np−2 k n0+...+np−2−sk−1 k−1 . A combinatorial proof of this claim is provided, and two convolution formulas due to Rothe are obtained as corollaries.Fil: Estrugo, Emiliano Juan José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Pastine, Adrián Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaCombinatorial Mathematics Society of Australasia2021-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150796Estrugo, Emiliano Juan José; Pastine, Adrián Gabriel; The number of s-separated k-sets in various circles; Combinatorial Mathematics Society of Australasia; The Australasian Journal of Combinatorics; 79; 3; 2-2021; 424-4362202-35181034-4942CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://ajc.maths.uq.edu.au/pdf/79/ajc_v79_p424.pdfinfo:eu-repo/semantics/altIdentifier/url/https://ajc.maths.uq.edu.au/?page=get_volumes&volume=79info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1805.01562info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:05:29Zoai:ri.conicet.gov.ar:11336/150796instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-02-26 10:05:30.147CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The number of s-separated k-sets in various circles
title The number of s-separated k-sets in various circles
spellingShingle The number of s-separated k-sets in various circles
Estrugo, Emiliano Juan José
S-Separation
N-Circle
K-Stras in Graphs
K-Sets
title_short The number of s-separated k-sets in various circles
title_full The number of s-separated k-sets in various circles
title_fullStr The number of s-separated k-sets in various circles
title_full_unstemmed The number of s-separated k-sets in various circles
title_sort The number of s-separated k-sets in various circles
dc.creator.none.fl_str_mv Estrugo, Emiliano Juan José
Pastine, Adrián Gabriel
author Estrugo, Emiliano Juan José
author_facet Estrugo, Emiliano Juan José
Pastine, Adrián Gabriel
author_role author
author2 Pastine, Adrián Gabriel
author2_role author
dc.subject.none.fl_str_mv S-Separation
N-Circle
K-Stras in Graphs
K-Sets
topic S-Separation
N-Circle
K-Stras in Graphs
K-Sets
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This article studies the number of ways of selecting k objects arranged in p circles of sizes n0,...,np−1 such that no two selected ones have less than s objects between them. If ni ≥ sk + 1 for all 0 ≤ i ≤ p − 1, this number is shown to be n0+...+np−2 k n0+...+np−2−sk−1 k−1 . A combinatorial proof of this claim is provided, and two convolution formulas due to Rothe are obtained as corollaries.
Fil: Estrugo, Emiliano Juan José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Pastine, Adrián Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
description This article studies the number of ways of selecting k objects arranged in p circles of sizes n0,...,np−1 such that no two selected ones have less than s objects between them. If ni ≥ sk + 1 for all 0 ≤ i ≤ p − 1, this number is shown to be n0+...+np−2 k n0+...+np−2−sk−1 k−1 . A combinatorial proof of this claim is provided, and two convolution formulas due to Rothe are obtained as corollaries.
publishDate 2021
dc.date.none.fl_str_mv 2021-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/150796
Estrugo, Emiliano Juan José; Pastine, Adrián Gabriel; The number of s-separated k-sets in various circles; Combinatorial Mathematics Society of Australasia; The Australasian Journal of Combinatorics; 79; 3; 2-2021; 424-436
2202-3518
1034-4942
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150796
identifier_str_mv Estrugo, Emiliano Juan José; Pastine, Adrián Gabriel; The number of s-separated k-sets in various circles; Combinatorial Mathematics Society of Australasia; The Australasian Journal of Combinatorics; 79; 3; 2-2021; 424-436
2202-3518
1034-4942
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ajc.maths.uq.edu.au/pdf/79/ajc_v79_p424.pdf
info:eu-repo/semantics/altIdentifier/url/https://ajc.maths.uq.edu.au/?page=get_volumes&volume=79
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1805.01562
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Combinatorial Mathematics Society of Australasia
publisher.none.fl_str_mv Combinatorial Mathematics Society of Australasia
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1858305171576061952
score 13.176822

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