Combinatorics

Table of contents

1. Identities
   1. Hockey-stick identity
   2. Vandermonde’s identity

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Identities

Hockey-stick identity

$$\sum_{i=r}^n {i \choose r} = {n+1 \choose r+1}$$

$$\sum_{i=0}^{n-r} {i + r \choose i} = {n+1 \choose n - r}$$

Vandermonde’s identity

$${m + n \choose r} = \sum_{k=0}^r {m \choose k}{n \choose r - k}$$