New combinatorial interpretations of r-Whitney and r-Whitney-Lah numbers

T. A. Dowling introduced Whitney numbers of the first and second kind concerning the so-called Dowling lattices of finite groups. It turned out that they are generalizations of Stirling numbers. Later, I. Mező defined r-Whitney numbers as common generalizations of Whitney numbers and r-Stirling numbers. Additionally, G.-S. Cheon and J.-H. Jung defined r-Whitney-Lah numbers. In our paper, we give new combinatorial interpretations of r-Whitney and r-Whitney-Lah numbers, which correspond better with the combinatorial definitions of Stirling, r-Stirling, Lah and r-Lah numbers. These allow us to explain their properties in a purely combinatorial manner, as well as derive several new identities