Suppose that $\lambda,\mu$ are integer partitions, with conjugates $\lambda^*,\mu^*$. Could you help me to prove the following formula, please?
$\sum_{i,j}\mathrm{min}(\lambda_i,\mu_j)=\sum_k\lambda^*_k\mu^*_k$
Suppose that $\lambda,\mu$ are integer partitions, with conjugates $\lambda^*,\mu^*$. Could you help me to prove the following formula, please?
$\sum_{i,j}\mathrm{min}(\lambda_i,\mu_j)=\sum_k\lambda^*_k\mu^*_k$