Pochhammer Symbol - Connection Coefficients

Connection Coefficients

Since the falling factorials are a basis for the polynomial ring, we can re-express the product of two of them as a linear combination of falling factorials:

The coefficients of the (x)_m+n-k, called connection coefficients, have a combinatorial interpretation as the number of ways to identify (or glue together) k elements each from a set of size m and a set of size n.