The (r1,...,rp)-Bell polynomials

Abstract

In a previous paper, Mihoubi et al. introduced the (r 1 , . . . , r p )-Stirling numbers and the (r 1 , . . . , r p )-Bell polynomials and gave some of their combinatorial and algebraic properties. These numbers and polynomials generalize, respectively, the r-Stirling numbers of the second kind introduced by Broder and the r-Bell polynomials introduced by Mező. In this paper, we prove that the (r 1 , . . . , r p )-Stirling numbers of the second kind are log-concave. We also give generating functions and generalized recurrences related to the (r 1 , . . . , r p )-Bell polynomials.