Abstract
Let G be a permutation group acting on a set Ω of size n∈ℕ and let 1≤k<(n−1)/2. Livingstone and Wagner proved that the number of orbits of G on k-subsets of Ω is less than or equal to the number of orbits on (k+1)-subsets. We investigate the cases when equality occurs.
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Bundy, D., Hart, S. The case of equality in the Livingstone-Wagner Theorem. J Algebr Comb 29, 215–227 (2009). https://doi.org/10.1007/s10801-008-0130-7
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DOI: https://doi.org/10.1007/s10801-008-0130-7