Bracket notation

[crestu]

In a mathematics article, A few riddles behind Rolle's theorem, I read:

"... we can associate the arrangement A_f of all \(\displaystyle \left( {\matrix{
{n + 1} \cr
2 \cr

} } \right)\) zeros {x_l⁽ⁱ⁾} of fⁱ ..."

It's at the bottom of page 1 of the article if the above quote isn't clear enough.

Can anyone tell me what the '\(\displaystyle \left( {\matrix{
{n + 1} \cr
2 \cr

} } \right)\)' notation means?

 

[soroban]

Hello, crestu!

Can anyone tell me what \(\displaystyle \begin{pmatrix}n + 1 \\ 2\end{pmatrix}\) means?

It is a "combination" number.

It means the same as "n + 1, choose 2" ... or C(n+1, 2)

In either case, it equals: \(\displaystyle \L\;\frac{(n+1)!}{2!\.(n-1)!} \;=\;\frac{n(n+1)}{2}\)

 

[crestu]

Exactely what I needed to know, thanks soroban.