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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.
Document Type
Article
Publication Date
2-16-2017
Funding Information
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).
Repository Citation
Cai, Yue; Ehrenborg, Richard; and Readdy, Margaret, "q-Stirling Identities Revisited" (2017). Mathematics Faculty Publications. 31.
https://uknowledge.uky.edu/math_facpub/31
Notes/Citation Information
Published in The Electronic Journal of Combinatorics, v. 25, issue 1, paper #P1.37, p. 1-18.
The publisher has granted the permission for posting the article here.