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The case of equality in the Livingstone-Wagner Theorem |
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| Authors: | David Bundy Sarah Hart |
| Institution: | 1.Mathematisches Seminar,Universit?t zu Kiel,Kiel,Germany;2.School of Economics, Mathematics and Statistics,Birkbeck, University of London,London,UK |
| 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. |
| Keywords: | Livingstone-Wagner Theorem Permutation groups Orbits Partitions |
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