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.
Yue Cai supported by the Simons Foundation (grant #206001) for two research visits to Princeton University to work with the second and third author.
Richard Ehrenborg supported by NSA grant H98230-13-1-0280 and a grant from the Simons Foundation (#429370 to Richard Ehrenborg).
Margaret Readdy supported by grants from the Simons Foundation (#206001 and #422467 to Margaret Readdy).
Cai, Yue; Ehrenborg, Richard; and Readdy, Margaret, "q-Stirling Identities Revisited" (2017). Mathematics Faculty Publications. 31.