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.

Read more about this topic:  Pochhammer Symbol

Famous quotes containing the word connection:

    “We will have to give up the hope that, if we try hard, we somehow will always do right by our children. The connection is imperfect. We will sometimes do wrong.”
    —Judith Viorst (20th century)