Abstract
We give a new q-(1 + q)-analogue of the Gaussian coefficient, also known as the q- binomial which, like the original q-binomial [n/k]q, is symmetric in k and n-k. We show this q-(1+q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the q-binomial.
| Original language | English |
|---|---|
| Article number | 16.7.8 |
| Journal | Journal of Integer Sequences |
| Volume | 19 |
| Issue number | 7 |
| State | Published - Jan 1 2016 |
Bibliographical note
Funding Information:The authors thank the referee for helpful comments. This work was partially supported by a grant from the Simons Foundation (#206001 to Margaret Readdy).
Publisher Copyright:
© 2016, University of Waterloo. All rights reserved.
Keywords
- Birkhoff transform
- Distributive lattice
- Poset decomposition
- Q-analogue
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics