Skip to main

Inicio / Mathematics (thesaurus)

Mathematics (thesaurus)

mathematical analysis > combinatorics > Vandermonde's identity

algebra > combinatorics > Vandermonde's identity

algebra > elementary algebra > identity > Vandermonde's identity

Término preferido

Vandermonde's identity

In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients:

${\\displaystyle {m+n \\choose r}=\\sum _{k=0}^{r}{m \\choose k}{n \\choose r-k}}$

for any nonnegative integers r, m, n. The identity is named after Alexandre-Théophile Vandermonde (1772), although it was already known in 1303 by the Chinese mathematician Zhu Shijie.
There is a q-analog to this theorem called the q-Vandermonde identity.
Vandermonde's identity can be generalized in numerous ways, including to the identity

${\\displaystyle {n_{1}+\\dots +n_{p} \\choose m}=\\sum _{k_{1}+\\cdots +k_{p}=m}{n_{1} \\choose k_{1}}{n_{2} \\choose k_{2}}\\cdots {n_{p} \\choose k_{p}}.}$

Vandermonde's convolution

identité de Vandermonde

francés
formule de convolution

URI

http://data.loterre.fr/ark:/67375/PSR-PJ28VRBP-W

Descargue este concepto:

RDF/XML TURTLE JSON-LD Creado 13/7/23, última modificación 13/7/23