A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions
Copyright policy )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 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].
- California State University, San Bernardino United States
- University of Seville Spain
- California State University System United States
- Simón Bolívar University Venezuela
Symmetric functions and generalizations, Vector symmetric function, Gessel map, Multi symmetric function, vector symmetric functions, MacMahon symmetric functions, Hopf algebras (associative rings and algebras), Gessel maps, Hopf algebras, formal power series, multi-symmetric functions, MacMahon symmetric function
Symmetric functions and generalizations, Vector symmetric function, Gessel map, Multi symmetric function, vector symmetric functions, MacMahon symmetric functions, Hopf algebras (associative rings and algebras), Gessel maps, Hopf algebras, formal power series, multi-symmetric functions, MacMahon symmetric function
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