Explicit formulas for the Dumont-Foata polynomial |
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Authors: | L Carlitz |
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Institution: | Department of Mathematics, Duke University, Durham, NC 27706, USA |
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Abstract: | Dumont and Foata have defined a polynomial Fn(x, y, z) recursively. They proved that Fn(x, y, z) is symmetric in x, y, z and that Fn(1, 1, 1) = G2n+2 the Genocchi number. Moreover, they gave an elegant combinatorial interpretation for the coefficients of Fn(x, y, z). In the present paper explicit formulas and generating functions for Fn(x, y, z) are obtained. |
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