A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions

摘要

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 [18,19].