A new notion of transitivity for groups and sets of permutations

William J. Martin, Bruce E. Sagan

Let $\Omega =\{1,2,...,n\}$ where $n\ge 2$. The {\em shape} of an ordered set partition $P=(P_1,...,P_k)$ of $\Omega$ is the integer partition $\lambda =({\lambda }_1,...,{\lambda }_k)$ defined by ${\lambda }_i=|P_i|$. Le…