q-Extension of Fubini Numbers

Abstract

In this paper we define a q-extension of Fubini numbers which we call q-Fubini numbers, and generalized q-Fubini numbers of order r. Using the p-adic Laplace transform and p-adic integration, we obtain these numbers as moments of appropriate p-adicmeasures. Then we establish some identities and congruences for these numbers. We establish also a relationship between generalized q-Fubini numbers of order r and q-Fubini numbers. Further, as done in previous works we introduce a concept of generalized q-Fubini numbers, attached to a continuous p^ℓℤ_p-invariant function ψ defined on ℤ_p. These numbers are also the moments of appropriate p-adic measures, we obtain identities and congruences which generalize those associated to q-Fubini numbers.