Journal of Integer Sequences, Vol. 19 (2016), Article 16.7.8

The Gaussian Coefficient Revisited

Richard Ehrenborg and Margaret A. Readdy
Department of Mathematics
University of Kentucky
Lexington, KY 40506-0027


We give a new q-(1+q)-analogue of the Gaussian coefficient, also known as the q-binomial which, like the original q-binomial $\genfrac{[}{]}{0pt}{}{n}{k}_q$, 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.

Full version:  pdf,    dvi,    ps,    latex    

Received May 19 2016; revised versions received August 31 2016; September 8 2016. Published in Journal of Integer Sequences, September 11 2016.

Return to Journal of Integer Sequences home page