@MISC{Deza80onpermutation, author = {M. Deza}, title = { ON PERMUTATION CLIQUES}, year = {1980} }

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Abstract

The symmetric group S, is a metric space with distance d(a, b) = IE(a-'b) ( where E(c) is the set of points moved by c E S,. Let L be a given subset of {I. 2,..., n}, a permutation clique A = A(L, n) is any subset A c S, with d(a, b)EL whenever a, b EA, a # b. We give a framework of new and known information on some special A = A(L, n): maximal, largest, largest subgroups of S,, subscheme of Hamming metric scheme, permutation geometry and some other problems related to this metric space. Some links with classical problems of classification of permutation groups and with extrernal problems on finite sets are given.