Let $\lambda$ be a partition of $n$ ($n=\lambda_1+\lambda_2+\cdots + \lambda_k$ and $\lambda_1\ge \lambda_2\ge\cdots$).
There is an ordering on the collection of all the $\lambda$-tabloids:
Let $\{t_1\}$ and $\{t_2\}$ be two $\lambda$-tabloids. We sat $\{t_1\}<\{t_2\}$ if there is an $i$ such that
$i$ is in higher row of $\{t_1\}$ than $\{t_2\}$
for all $j>i$, the entry $j$ lies in same row of $\{t_1\}$ and $\{t_2\}$.
Q.0 Is there any other equivalent version of this ordering? (I didn't get what we want to say through this ordering?)
Q.1 For what purpose this ordering of tabloids is important in the representations of symmetric groups?
Q.2 Since $\lambda$-tabloids are canonically in bijection with subgroups of $S_n$ of the form $S_{\lambda_1}\times S_{\lambda_2}\times \cdots \times S_{\lambda_k}$, so on the {\it subgroup level}, what the above ordering corresponds? What the about ordering says in terms of subgroups?