We consider the set of permutations all of whose descents are from an even value to an even value. Proving a conjecture of Kitaev and Remmel, we show that these permutations are enumerated by Genocchi numbers, hence equinumerous to Dumont permutations of the first (and second) kind, and thus may be called Dumont permutations of the third kind. We also define the related Dumont permutations of t...

Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute value is given by |x|p = p−r where x = p t s with (t, p) = (s, p) = (t, s) = 1. When one talk...

Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp, will, respectively, denote the ring of p-adic integers, the field, of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp such that |p|p p−νp p 1/p see 1–16 . As well-known definition, the Euler numbers and Genocchi number...

In this paper we provide an explicit formula for calculating the boolean number of a Ferrers graph. By previous work of the last two authors, this determines the homotopy type of the boolean complex of the graph. Specializing to staircase shapes, we show that the boolean numbers of the associated Ferrers graphs are the Genocchi numbers of the second kind, and obtain a relation between the Legen...

Ferrers graphs are bipartite graphs that correspond naturally to Ferrers shapes. In this paper, we determine the homotopy type of the boolean complex of Ferrers graphs. Previous work of the last two authors shows that the boolean complex of a graph is a wedge of spheres of maximal dimension. Thus the homotopy type of this complex depends entirely on the number of spheres in the wedge sum, calle...