Covering radius for sets of permutations
Copyright policy )Covering radius for sets of permutations
The authors study the covering radius of sets of permutations with respect to the Hamming distance. In particular, they define \(f(n,s)\) to be the smallest integer \(m\) for which there is a set of \(m\) permutations in \(S_n\) with covering radius \(r \leq n-s\). The authors find an exact formula for \(f(n,1)\) and bounds on \(f(n,s)\) for \(s>1\). In the case when the set of permutations forms a group, they give necessary and sufficient conditions for the covering radius to be exactly \(n\). They also provide some results on the covering radius for several specific groups.
- University of London United Kingdom
- Australian National University Australia
- Charles Darwin University Australia
- Queen Mary University of London United Kingdom
- UNIVERSITY OF LONDON United Kingdom
permutations, 511, 512, Dominating sets, steiner triple systems, Theoretical Computer Science, dominating sets, Discrete Mathematics and Combinatorics, Steiner triple systems, Combinatorial aspects of packing and covering, minkowski planes, affine planes, Permutations, words, matrices, Affine planes, covering radius, Minkowski planes, Permutations, Covering radius, latin squares, multiply transitive groups, Latin squares, Orthogonal arrays, Latin squares, Room squares, Multiply transitive groups
permutations, 511, 512, Dominating sets, steiner triple systems, Theoretical Computer Science, dominating sets, Discrete Mathematics and Combinatorics, Steiner triple systems, Combinatorial aspects of packing and covering, minkowski planes, affine planes, Permutations, words, matrices, Affine planes, covering radius, Minkowski planes, Permutations, Covering radius, latin squares, multiply transitive groups, Latin squares, Orthogonal arrays, Latin squares, Room squares, Multiply transitive groups
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