Q-Vandermonde Identity

Q-Vandermonde Identity

In mathematics, in the field of combinatorics, the q-Vandermonde identity is a q-analogue of the Chu-Vandermonde identity. Using standard notation for q-binomial coefficients, the identity states that

\binom{m + n}{k}_{\!\!q} = \sum_{j} \binom{m}{k - j}_{\!\!q} \binom{n}{j}_{\!\!q} q^{j(m-k+j)}.

(The nonzero contributions to this sum come from values of j such that the q-binomial coefficients on the right side are nonzero, that is, .)

Read more about Q-Vandermonde Identity:  Other Conventions, Proofs of The Identity

Famous quotes containing the word identity:

    “Adultery is the vice of equivocation.
    It is not marriage but a mockery of it, a merging that mixes love and dread together like jackstraws. There is no understanding of contentment in adultery.... You belong to each other in what together you’ve made of a third identity that almost immediately cancels your own. There is a law in art that proves it. Two colors are proven complimentary only when forming that most desolate of all colors—neutral gray.”
    —Alexander Theroux (b. 1940)