Proceedings of Symposia in Pure Mathematics, vol. 34, 1979,
American Mathematical Society, Providence
(Relations between Combinatorics and other parts of Mathematics)
[1978. Columbus], p. 163-179.
Dominique Foata and Adriano M. Garsia
The Mehler Formulas for Hermite Polynomials
Abstract.
The multilinear expansion of the Mehler formula found by Slepian is proved combinatorially by using the partitional complex method.
The combinatorial structures involved are the so-called n-involutionary graphs. They are enumerated in two different manners:
first, globally, then, as the exponential of their connected components.
lt is shown that these two enumerations make up the left and right side members of the formula to be proved.
foata@unistra.fr
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