q-Stirling Identities Revisited
Keywords: q-Analogues, q-Stirling numbers, Restricted growth words, Poset decomposition
AbstractWe 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.