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:
“We should always remember that the work of art is invariably the creation of a new world, so that the first thing we should do is to study that new world as closely as possible, approaching it as something brand new, having no obvious connection with the worlds we already know. When this new world has been closely studied, then and only then let us examine its links with other worlds, other branches of knowledge.”
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