q-Stirling Identities Revisited

Authors

Yue Cai, Texas A&M University
Richard Ehrenborg, University of KentuckyFollow
Margaret Readdy, University of KentuckyFollow

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

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.

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