Finite Permutation Groups with Few Orbits Under the Action on the Power Set

Alexander Betz, Max Chao-Haft, Ting Gong +3

We study the orbits under the natural action of a permutation group $G\subseteq S_n$ on the powerset $\mathcal{P}(\{1,\dots ,n\})$. The permutation groups having exactly $n+1$ o…