$q$-Stirling numbers revisited
Combinatorics
2019-09-25 v1
Abstract
We give combinatorial proofs of -Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the -Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel -Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.
Cite
@article{arxiv.1706.06623,
title = {$q$-Stirling numbers revisited},
author = {Yue Cai and Richard Ehrenborg and Margaret A. Readdy},
journal= {arXiv preprint arXiv:1706.06623},
year = {2019}
}
Comments
18 pages