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 
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/
@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},
     year = {2004},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_3_a7/}
}
TY  - JOUR
AU  - V. P. Voronin
TI  - On average and typical values of sums of pairwise distances for subsets of vertices of the $n$-dimensional unit cube
JO  - Diskretnaya Matematika
PY  - 2004
SP  - 141
EP  - 152
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_2004_16_3_a7/
LA  - ru
ID  - DM_2004_16_3_a7
ER  - 
%0 Journal Article
%A V. P. Voronin
%T On average and typical values of sums of pairwise distances for subsets of vertices of the $n$-dimensional unit cube
%J Diskretnaya Matematika
%D 2004
%P 141-152
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/DM_2004_16_3_a7/
%G ru
%F DM_2004_16_3_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Zilberman B. S., “O raspolozhenii zaryadov v vershinakh edinichnogo $n$-mernogo kuba”, Dokl. AN SSSR, 149:3 (1963), 546–549 | MR

[2] Kruglova T. N., “Ob asimptoticheskom metode resheniya zadachi o zaryadakh”, Problemy kibernetiki, 13 (1965), 29–44

[3] Leontev V. K., “Asimptoticheski ustoichivye raspolozheniya zaryadov v vershinakh edinichnogo $n$-mernogo kuba”, Problemy kibernetiki, 23 (1970), 29–42 | MR

[4] Perina E. V., “O mnozhestvakh vershin $n$-mernogo edinichnogo kuba s maksimalnoi energiei”, Problemy kibernetiki, 27 (1974), 279–292 | MR

[5] Gavrilov G. P., Sapozhenko A. A., Zadachi i uprazhneniya po kursu diskretnoi matematiki, Nauka, Moskva, 1992 | MR | Zbl

[6] Voronin V. P., “O mnozhestvakh vershin $N$-mernogo edinichnogo kuba s minimalnoi summoi poparnykh rasstoyanii”, Voprosy kibernetiki. Kombinatornyi analiz i teoriya grafov, Izd-vo Nauchnogo soveta po kompleksnoi probleme “Kibernetika” AN SSSR, Moskva, 1980, 48–57