Geodesic
The case of equality in the Livingstone-Wagner theorem.
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 215-227.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a permutation group acting on a set $\Omega $of size $n\in \Bbb N$ and let $1\leq k( n - 1)/2$. Livingstone and Wagner proved that the number of orbits of $G$ on $k$-subsets of $\Omega $is less than or equal to the number of orbits on $( k+1)$-subsets. We investigate the cases when equality occurs.
Keywords: keywords livingstone-wagner theorem, permutation groups, orbits, partitions 
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     author = {Bundy, David and Hart, Sarah},
     title = {The case of equality in the {Livingstone-Wagner} theorem.},
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Bundy, David; Hart, Sarah. The case of equality in the Livingstone-Wagner theorem.. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 2, pp. 215-227. http://geodesic.mathdoc.fr/item/JAC_2009__29_2_a2/