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A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions
Mercedes H. Rosas1, Gian-Carlo Rota and Joel Stein2
1Departamento de Matematicas, Universidad Simon Bolivar, Apdo 89000, Caracas, Venezuela
mrosas@usb.ve
2Department of Mathematics, California State University at San Bernardino, San Bernardino CA, USA
jstein@csusb.edu
Annals of Combinatorics 6 (2) p.195-207 June, 2002
AMS Subject Classification: 16W30, 05E05
Abstract:
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 function relying on the construction of a Hopf algebra from any alphabet of neutral letters obtained in [18,19].
Keywords: MacMahon symmetric function, vector symmetric function, multi symmetric function, Gessel map

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