Math. Zeitschrift, 137, 1974, 257-264.
Dominique Foata and Volker Strehl
Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers
Abstract.
In a recent note the first author has announced the discovery of a family of transformation groups (G(n)) (n>0), which have the following property; G(n) acts on the n! elements of the symmetric group S(n) and the number of its orbits is equal to the n-th tangent or secant number, according as n is odd of even. The purpose of this paper is to give a complete description of these groups. Applications to enumeration problems will appear in a subsequent paper.
foata@unistra.fr, volker.strehl@fau.de
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