# Young tableaux of shape lambda.

• April 29th 2013, 04:10 PM
vercammen
Young tableaux of shape lambda.
Consider the partition $\lambda=(m,n-m)$ of $n$ (thus $2m \ge n$.)

The number of Young
tableaux of shape $\lambda$ is given by
$f_{(m,n-m)} = \binom nm - \binom{n}{m+1}$

a) Prove this using the hook-length formula.

b) Prove this using induction on $n$