Specializations of MacMahon symmetric functions and the polynomial algebra

Authors:
Mercedes H. Rosas
Affiliations:
Departamento de Matemáticas, Universidad Simón Bolívar, Apdo. Postal 89000, Caracas, Venezuela
Venue:
Discrete Mathematics
Year:
2002

Citing 2
Cited 0

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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. We use a combinatorial construction of the different bases of the vector space of MacMahon symmetric functions found by the author to obtain their image under the principal specialization: the powers, rising and falling factorials. Then, we compute the connection coefficients of the different polynomial bases in a combinatorial way.