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A MacMahon symmetric function is a formal power series in a nite number of al- phabets 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 func- tions relying on the construction of a Hopf algebra from any alphabet of neutral letters obtained in (18, 19).

A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions