Gaussian polynomials

For an indeterminate q and integers nm0 we define the following:

(a) (m)q=qm-1+qm-2++1 for m>0,

(b) (m!)q=(m)q(m-1)q(1)q for m>0, and (0!)q=1,

(c) (nm)q=(n!)q(m!)q((n-m)!)q. If m>n then we define (nm)q=0.

Note: if we replace q with 1, then we obtain the familiar integers, factorialsMathworldPlanetmath, and binomial coefficients. Specifically,

(a) (m)1=m,

(b) (m!)1=m!,

(c) (nm)1=(nm).

(d) (mm)q=1.

Title Gaussian polynomials
Canonical name GaussianPolynomials
Date of creation 2013-03-22 11:49:49
Last modified on 2013-03-22 11:49:49
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 10
Author mathcam (2727)
Entry type Definition
Classification msc 05A30
Classification msc 05A10
Classification msc 16S36
Classification msc 26A09
Classification msc 26A18
Classification msc 15A04
Synonym q-binomial coefficients
Related topic ContentOfPolynomial