q-Stirling Identities Revisited

Abstract

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 Garsia and Remmel 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.