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.
Read more about this topic: Pochhammer Symbol
Famous quotes containing the word connection:
“The connection between our knowledge and the abyss of being is still real, and the explication must be not less magnificent.”
—Ralph Waldo Emerson (1803–1882)