Combinatorial proof for a stability property of plethysm coefficients

Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, pr...

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Detalhes bibliográficos
Autores: Colmenarejo Hernando, Laura, Briand, Emmanuel
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2014
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87750
Acesso em linha:https://hdl.handle.net/11441/87750
https://doi.org/10.1016/j.endm.2014.08.007
Access Level:acceso abierto
Palavra-chave:Combinatorial representation theory
Symmetric functions
Plethysm
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spelling Combinatorial proof for a stability property of plethysm coefficientsColmenarejo Hernando, LauraBriand, EmmanuelCombinatorial representation theorySymmetric functionsPlethysmPlethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose plethysm coefficients as a alternating sum of terms counting integer points in poly- topes, and exhibit bijections between these sets of integer points.Ministerio de Ciencia e Innovación MTM2010–19336Junta de Andalucía FQM–333Junta de Andalucía P12–FQM–2696ElsevierMatemática Aplicada I2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87750https://doi.org/10.1016/j.endm.2014.08.007reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Notes in Discrete Mathematics, 46 (september 2014), 43-50.MTM2010–19336FQM–333P12–FQM–2696https://www.sciencedirect.com/science/article/pii/S1571065314000080info:eu-repo/semantics/openAccessoai:idus.us.es:11441/877502026-06-17T12:51:07Z
dc.title.none.fl_str_mv Combinatorial proof for a stability property of plethysm coefficients
title Combinatorial proof for a stability property of plethysm coefficients
spellingShingle Combinatorial proof for a stability property of plethysm coefficients
Colmenarejo Hernando, Laura
Combinatorial representation theory
Symmetric functions
Plethysm
title_short Combinatorial proof for a stability property of plethysm coefficients
title_full Combinatorial proof for a stability property of plethysm coefficients
title_fullStr Combinatorial proof for a stability property of plethysm coefficients
title_full_unstemmed Combinatorial proof for a stability property of plethysm coefficients
title_sort Combinatorial proof for a stability property of plethysm coefficients
dc.creator.none.fl_str_mv Colmenarejo Hernando, Laura
Briand, Emmanuel
author Colmenarejo Hernando, Laura
author_facet Colmenarejo Hernando, Laura
Briand, Emmanuel
author_role author
author2 Briand, Emmanuel
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
dc.subject.none.fl_str_mv Combinatorial representation theory
Symmetric functions
Plethysm
topic Combinatorial representation theory
Symmetric functions
Plethysm
description Plethysm coefficients are important structural constants in the representation the- ory of the symmetric groups and general linear groups. Remarkably, some sequences of plethysm coefficients stabilize (they are ultimately constants). In this paper we give a new proof of such a stability property, proved by Brion with geometric representation theory techniques. Our new proof is purely combinatorial: we decompose plethysm coefficients as a alternating sum of terms counting integer points in poly- topes, and exhibit bijections between these sets of integer points.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/87750
https://doi.org/10.1016/j.endm.2014.08.007
url https://hdl.handle.net/11441/87750
https://doi.org/10.1016/j.endm.2014.08.007
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Notes in Discrete Mathematics, 46 (september 2014), 43-50.
MTM2010–19336
FQM–333
P12–FQM–2696
https://www.sciencedirect.com/science/article/pii/S1571065314000080
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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