The Gaussian coefficient revisited
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 []0ptnkq, 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.
0