 In particular "X"(1) is the cardinality of the set "X", and for that reason "X"("q") is regarded as a generating function for "X".The "q"-binomial coefficient

is the polynomial in "q" defined by

It is easily seen that its value at "q" = 1 is the usual binomial coefficient formula_3, so it is a generating function for the subsets of {1, 2, ..., "n"} of size "k".These subsets carry a natural action of the cyclic group "C" of order "n" which acts by adding 1 to each element of the set, modulo "n".