# ENS Paris preparation

Good morning everyone, I'm a french student who wants to pass the contest of ENS Ulm I need specific problems and exercises, I hope someone would help me here... I know there are many french student in this forum. Let's start with this difficult oral which was given in ENS Paris:

What is the dimension of vector space of symmetric polynomials with $k$ variables and degree at most $n$ ?

I've seen this problem in this forum but no convincing answer were given. Thanks for your help, I'll be so much thankful.

• Quel est le degré en général d'un polynôme non nul à plusieurs variables ? – Maman Jun 19 '17 at 1:47