Intersection theorems in permutation groups

Abstract

The Hamming distance between two permutations of a finite setX is the number of elements ofX on which they differ. In the first part of this paper, we consider bounds for the cardinality of a subset (or subgroup) of a permutation groupP onX with prescribed distances between its elements. In the second part. We consider similar results for sets ofs-tuples of permutations; the role of Hamming distance is played by the number of elements ofX on which, for somei, the ith permutations of the two tuples differ.

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Cameron, P.J., Deza, M. & Frankl, P. Intersection theorems in permutation groups. Combinatorica 8, 249–260 (1988). https://doi.org/10.1007/BF02126798

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AMS subject classification (1980)

  • 20B99