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Generalized Dumont-Foata polynomials. (Polynômes de Dumont-Foata généralisés.) (French) Zbl 0856.05005

Summary: We study a sequence of polynomials with six variables which is an extension of Dumont-Foata polynomials. In particular we prove the three recent Dumont conjectures on the ternary symmetries related to Genocchi numbers.

MSC:

05A15 Exact enumeration problems, generating functions
05E35 Orthogonal polynomials (combinatorics) (MSC2000)
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