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Total Relative Displacement of Permutations

✍ Scribed by Wayne Aitken

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
169 KB
Volume
87
Category
Article
ISSN
0097-3165

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✦ Synopsis

Let , be a permutation of the set [1, 2, 3, ..., N]. We call the sum $ , = ||i& j | &|,(i)&,( j)| | the total relative displacement (where the sum is over all i, j such that 1 i< j N). Chartrand, Gavlas, and VanderJagt conjectured that among permutations of [1, ..., N] the smallest positive value of $ , is 2N&4. We prove this result and develop a general theory for small values of $ , for permutations and, more generally, for functions S Γ„ Z with finite domain S/Z.

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