TY - JOUR

T1 - A generalization of the r-Whitney numbers of the second kind

AU - Mansour, Toufik

AU - Ramírez, José L.

AU - Shattuck, Mark

PY - 2017

Y1 - 2017

N2 - In this paper, we consider a (p,q)-generalization of the r-Whitney numbers of the second kind and of the associated r-Dowling polynomials. We obtain generalizations of some earlier results for these numbers, including recurrence and generating function formulas, that reduce to them when p=q=1. Furthermore, some of our results appear to be new in the case p=q=1 and thus yield additional formulas for the r-Whitney numbers. As a consequence, some new identities are obtained for the q-Stirling and r-Whitney numbers. In addition, the log-concavity of our generalized Whitney numbers is shown for certain values of the parameters p and q. Finally, we introduce (p,q)-Whitney matrices of the second kind and study some of their properties.

AB - In this paper, we consider a (p,q)-generalization of the r-Whitney numbers of the second kind and of the associated r-Dowling polynomials. We obtain generalizations of some earlier results for these numbers, including recurrence and generating function formulas, that reduce to them when p=q=1. Furthermore, some of our results appear to be new in the case p=q=1 and thus yield additional formulas for the r-Whitney numbers. As a consequence, some new identities are obtained for the q-Stirling and r-Whitney numbers. In addition, the log-concavity of our generalized Whitney numbers is shown for certain values of the parameters p and q. Finally, we introduce (p,q)-Whitney matrices of the second kind and study some of their properties.

U2 - 10.4310/joc.2017.v8.n1.a2

DO - 10.4310/joc.2017.v8.n1.a2

M3 - מאמר

SN - 2156-3527

VL - 8

SP - 29

EP - 55

JO - Journal of Combinatorics

JF - Journal of Combinatorics

IS - 1

ER -