Geodesic
On average and typical values of sums of pairwise distances for subsets of vertices of the $n$-dimensional unit cube
Diskretnaya Matematika, Tome 16 (2004) no. 3, pp. 141-152

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We study the question on average and typical values of sums of pairwise Hamming distances for subsets of vertices of the $n$-dimensional unit cube. We suggest an approach to the problem of evaluation of average and typical values of arbitrary functionals defined on subsets of a finite set as the sum of values assigned to ordered pairs of elements of this set; general formulas for this case are obtained. We find average and typical values of sums of pairwise distances in the case of all subsets of vertices of the $n$-dimensional unit cube and of sums of pairwise distances for subsets of vertices of fixed cardinality.This research was supported by the Russian Foundation for Basic Research, grant 01–01–00266Б. 
@article{DM_2004_16_3_a7,
     author = {V. P. Voronin},
     title = {On average and typical values of sums of pairwise distances for subsets of vertices of the $n$-dimensional unit cube},
     journal = {Diskretnaya Matematika},
     pages = {141--152},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_3_a7/}
}
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V. P. Voronin. On average and typical values of sums of pairwise distances for subsets of vertices of the $n$-dimensional unit cube. Diskretnaya Matematika, Tome 16 (2004) no. 3, pp. 141-152. http://geodesic.mathdoc.fr/item/DM_2004_16_3_a7/