A combinatorial overview of the Hopf algebra of MacMahon symmetric functions

A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction o...

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Detalles Bibliográficos
Autores: Rosas Celis, Mercedes Helena, Rota, Gian-Carlo, Stein, Joel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2002
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/46818
Acceso en línea:http://hdl.handle.net/11441/46818
https://doi.org/10.1007/PL00012586
Access Level:acceso abierto
Palabra clave:MacMahon symmetric function
Vector symmetric function
Multi symmetric function
Gessel map
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spelling A combinatorial overview of the Hopf algebra of MacMahon symmetric functionsRosas Celis, Mercedes HelenaRota, Gian-CarloStein, JoelMacMahon symmetric functionVector symmetric functionMulti symmetric functionGessel mapA MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction of a Hopf algebra from any alphabet of neutral letters obtained in [18 G.-C. Rota and J. Stein, Plethystic Hopf algebras, Proc. Natl. Acad. Sci. USA 91 (1994) 13057–13061. 19. G.-C. Rota and J. Stein, Plethystic algebras and vector symmetric functions, Proc. Natl. Acad. Sci. USA 91 (1994) 13062–13066].SpringerÁlgebraFQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones2002info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/46818https://doi.org/10.1007/PL00012586reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAnnals of Combinatorics, 6 (2), 195-207.http://download.springer.com/static/pdf/516/art%253A10.1007%252FPL00012586.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2FPL00012586&token2=exp=1475564844~acl=%2Fstatic%2Fpdf%2F516%2Fart%25253A10.1007%25252FPL00012586.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252FPL00012586*~hmac=f105e98f1288dcc38e81d9edb33e85209daea7fd240029d720faab7a9a56c789info:eu-repo/semantics/openAccessoai:idus.us.es:11441/468182026-06-17T12:51:07Z
dc.title.none.fl_str_mv A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
title A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
spellingShingle A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
Rosas Celis, Mercedes Helena
MacMahon symmetric function
Vector symmetric function
Multi symmetric function
Gessel map
title_short A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
title_full A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
title_fullStr A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
title_full_unstemmed A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
title_sort A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
dc.creator.none.fl_str_mv Rosas Celis, Mercedes Helena
Rota, Gian-Carlo
Stein, Joel
author Rosas Celis, Mercedes Helena
author_facet Rosas Celis, Mercedes Helena
Rota, Gian-Carlo
Stein, Joel
author_role author
author2 Rota, Gian-Carlo
Stein, Joel
author2_role author
author
dc.contributor.none.fl_str_mv Álgebra
FQM333: Algebra Computacional en Anillos no Conmutativos y Aplicaciones
dc.subject.none.fl_str_mv MacMahon symmetric function
Vector symmetric function
Multi symmetric function
Gessel map
topic MacMahon symmetric function
Vector symmetric function
Multi symmetric function
Gessel map
description A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction of a Hopf algebra from any alphabet of neutral letters obtained in [18 G.-C. Rota and J. Stein, Plethystic Hopf algebras, Proc. Natl. Acad. Sci. USA 91 (1994) 13057–13061. 19. G.-C. Rota and J. Stein, Plethystic algebras and vector symmetric functions, Proc. Natl. Acad. Sci. USA 91 (1994) 13062–13066].
publishDate 2002
dc.date.none.fl_str_mv 2002
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 http://hdl.handle.net/11441/46818
https://doi.org/10.1007/PL00012586
url http://hdl.handle.net/11441/46818
https://doi.org/10.1007/PL00012586
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Annals of Combinatorics, 6 (2), 195-207.
http://download.springer.com/static/pdf/516/art%253A10.1007%252FPL00012586.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2FPL00012586&token2=exp=1475564844~acl=%2Fstatic%2Fpdf%2F516%2Fart%25253A10.1007%25252FPL00012586.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252FPL00012586*~hmac=f105e98f1288dcc38e81d9edb33e85209daea7fd240029d720faab7a9a56c789
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 Springer
publisher.none.fl_str_mv Springer
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
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