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Maximal total absolute displacement of a permutation

✍ Scribed by Lon H. Mitchell

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
164 KB
Volume
274
Category
Article
ISSN
0012-365X

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✦ Synopsis

We determine those permutations that have maximal absolute total displacement on a ΓΏnite subset of real numbers, and give some corollaries.

πŸ“œ SIMILAR VOLUMES

Total Relative Displacement of Permutati
Total Relative Displacement of Permutations
✍ Wayne Aitken πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 169 KB

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

Total relative displacement of vertex pe
Total relative displacement of vertex permutations of K
✍ K. B. Reid πŸ“‚ Article πŸ“… 2002 πŸ› John Wiley and Sons 🌐 English βš– 167 KB

## Abstract Let Ξ± denote a permutation of the __n__ vertices of a connected graph __G__. Define Ξ΄~Ξ±~(__G__) to be the number $\sum |d(x,y)-d(\alpha (x),\alpha(y))|$, where the sum is over all the $\left({n \atop 2} \right)$ unordered pairs of distinct vertices of __G__. The number Ξ΄~Ξ±~(__G__) is ca