2 problems

Let $n$ be a positive integer, let $\mu$ and $\mu'$ be partitions of $n$, and let $\tau$ be a partition of $n$. Write … For partitions of $n$, let $\mu'\trianglelefteq\mu$ mean tha…

Let $n$ be a positive integer, let $\mu=(\mu_1,\mu_2,\dots)$ be a partition of $n$, and let $\tau$ be a partition of $n$. For triples of partitions define … where…