Re: [math-fun] Q-factorials

On Thu, 8 Jun 2006, Schroeppel, Richard wrote:

I've been playing with Q-factorials:

QF(0) == 1 QF(N+1) == QF(N) * (1 + Q + Q^2 + ... + Q^N).

There are people who make a living creating "q-analogs" of well-known functions, identities, etc. You can find some leads here: http://mathworld.wolfram.com/q-Analog.html My favorite is the q-binomial(n,k) which as q --> 1 goes to the usual binomial(n,k). Among other things q-binomial(n,k) is the number of k-dimensional subspaces of an n-dimensional vector space over a field with q elements. It is a polynomial in q and the coefficients have a combinatorial interpretation.