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
Descripción
Sumario: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].