English

$q$-Stirling numbers revisited

Combinatorics 2019-09-25 v1

Abstract

We give combinatorial proofs of qq-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz's identity, a new proof of the qq-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel qq-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.

Keywords

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

R2 v1 2026-06-22T20:24:27.448Z