\(q\)-Stirling identities revisited (Q1700805)

Summary: We give combinatorial proofs of \(q\)-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the \(q\)-Frobenius identity of \textit{A. M. Garsia} and \textit{J. B. Remmel} [J. Comb. Theory, Ser. A 41, 246--275 (1986; Zbl 0598.05007)] and of Ehrenborg's Hankel \(q\)-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.