I wonder if there exists a difference equation which (unique) solution is the q-binomial coefficient $\binom{n}{p}_{q}$ where $p$ is given. I have a mathematical object that I suspect that it is a q-binomial coefficient, but I don't know if there are equivalent conditions to conclude that object is or not a q-binomial.
difference equation for q-binomial
3
$\begingroup$
combinatorics
1 Answers
2
Yes, you have the "$q$-Pascal triangle" with boundary value 1 along the edges. See http://en.wikipedia.org/wiki/Gaussian_coefficient#Properties.