Vandermonde's Identity - Generalized Vandermonde's Identity

Generalized Vandermonde's Identity

If in the algebraic derivation above more than two polynomials are used, it results in the generalized Vandermonde's identity. For y + 1 polynomials:


\sum_{k_1+\dots +k_y = 0}^x {n\choose k_1} {n\choose k_2} {n\choose k_3} \cdots {n \choose x - \sum_{j = 1}^y k_j } = { \left( y + 1 \right) n \choose x}.

Read more about this topic:  Vandermonde's Identity

Famous quotes containing the words generalized and/or identity:

    One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.
    —H.L. (Henry Lewis)

    Personal change, growth, development, identity formation—these tasks that once were thought to belong to childhood and adolescence alone now are recognized as part of adult life as well. Gone is the belief that adulthood is, or ought to be, a time of internal peace and comfort, that growing pains belong only to the young; gone the belief that these are marker events—a job, a mate, a child—through which we will pass into a life of relative ease.
    Lillian Breslow Rubin (20th century)