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.

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Famous quotes containing the word connection:

    “The virtue of art lies in detachment, in sequestering one object from the embarrassing variety. Until one thing comes out from the connection of things, there can be enjoyment, contemplation, but no thought.”
    —Ralph Waldo Emerson (1803–1882)