  We define the $(q,\bar{\boldsymbol{\alpha}})$-Whitney numbers which are
reduced to the $\bar{\boldsymbol{\alpha}}$-Whitney numbers when
$q\rightarrow1$. Moreover, we obtain several properties of these numbers such
as explicit formulas, recurrence relations, generating functions, orthogonality
and inverse relations. Finally, we define the
$\bar{\boldsymbol{\alpha}}$-Whitney-Lah numbers as a generalization of the
$r$-Whitney-Lah numbers and we introduce their important basic properties.

Combinatorics