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A NEW NOTION OF TRANSITIVITY FOR GROUPS AND SETS OF PERMUTATIONS
2006
Journal of the London Mathematical Society
Let Ω = {1, 2, . . . , n} where n 2. The shape of an ordered set partition P = (P 1 , . . . , P k ) of Ω is the integer partition λ = (λ 1 , . . . , λ k ) defined by λ i = |P i |. Let G be a group of permutations acting on Ω. For a fixed partition λ of n, we say that G is λ-transitive if G has only one orbit when acting on partitions P of shape λ. A corresponding definition can also be given when G is just a set. For example, if λ = (n − t, 1, . . . , 1), then a λ-transitive group is the same
doi:10.1112/s0024610705022441
fatcat:tkdswyeyoje7hfe26cxpy6tsgq