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:
“Much is made of the accelerating brutality of young people’s crimes, but rarely does our concern for dangerous children translate into concern for children in danger. We fail to make the connection between the use of force on children themselves, and violent antisocial behavior, or the connection between watching father batter mother and the child deducing a link between violence and masculinity.”
—Letty Cottin Pogrebin (20th century)