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
)-analogue of the
Gaussian coefficient, also known as the
-binomial which, like the original q
is symmetric in k
We show this q
)-binomial is more compact than
the one discovered by Fu, Reiner, Stanton, and Thiem.
Underlying our q
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
Full version: pdf,
Received May 19 2016;
revised versions received August 31 2016; September 8 2016.
Published in Journal of Integer Sequences, September 11 2016.
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