Christian Krattenthaler,
Brandt Kronholm and Paul Marsh
An orthogonal view of Gaussian polynomials
(26 pages)
Abstract.
We establish an alternative, "perpendicular" collection of
generating functions for the coefficients of Gaußian
polynomials,
\qbin{N+m}{m}_q.
We provide a general characterization of these perpendicular
generating functions.
For small values of m, unimodality of the coefficients of Gaußian
polynomials is easily proved from these generating functions.
Additionally, we uncover new and surprising identities for the
differences of Gaußian polynomial coefficients, including a very
unexpected infinite family of congruences for coefficients of
\qbin{N+4}{4}_q.
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