A permutation π is said to be a Dumont permutation of the first kind if each even integer in π must be followed by a smaller integer, and each odd integer is either followed by a larger integer or is the last element of π (see, for example, www.theory.csc.uvic.ca/∼cos/inf/perm/Genocchi Info.html). In Duke Math. J. 41 (1974), 305–318, Dumont showed that certain classes of permutations on n lette...

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

A Genocchi permutation of 2n] is a permutation such that (2i?1) > 2i?1; (2i) 2i for all i 2 f1; 2; : : : ; 2ng. The purpose of this paper is to investigate the equidistribution of several bivariate statistics on the Genocchi permutations.