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.
| Original language | English |
|---|---|
| Journal | Electronic Journal of Combinatorics |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 16 2018 |
Bibliographical note
Funding Information:Supported by the Simons Foundation (grant #206001) for two research visits to Princeton University to work with the second and third author. † Supported by NSA grant H98230-13-1-0280 and a grant from the Simons Foundation(#429370 to Richard Ehrenborg). ‡ Supported by grants from the Simons Foundation(#206001 and #422467 to Margaret Readdy). The authors thank Dennis Stanton for directing us to the pair of identities of Carlitz discussed in Section 9. The authors would also like to thank the Princeton University Mathematics Department for its hospitality and support.
Funding Information:
∗Supported by the Simons Foundation (grant #206001) for two research visits to Princeton University to work with the second and third author. †Supported by NSA grant H98230-13-1-0280 and a grant from the Simons Foundation (#429370 to Richard Ehrenborg). ‡Supported by grants from the Simons Foundation (#206001 and #422467 to Margaret Readdy).
Publisher Copyright:
© 2018, Australian National University. All rights reserved.
Keywords
- Poset decomposition
- Q-Stirling numbers
- Q-analogues
- Restricted growth words
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics