The minimum length of a base for the symmetric group acting on partitions
A base for a permutation group, G, is a sequence of elements of its permutation domain whose stabiliser in G is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best...[Show more]
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|Source:||European Journal of Combinatorics|
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