Geodesic
On the number closure-type mappings
Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 85-97 
V. B. Alekseev. On the number closure-type mappings. Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 85-97. http://geodesic.mathdoc.fr/item/DM_2004_16_2_a5/
@article{DM_2004_16_2_a5,
     author = {V. B. Alekseev},
     title = {On the number closure-type mappings},
     journal = {Diskretnaya Matematika},
     pages = {85--97},
     year = {2004},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_2_a5/}
}
TY  - JOUR
AU  - V. B. Alekseev
TI  - On the number closure-type mappings
JO  - Diskretnaya Matematika
PY  - 2004
SP  - 85
EP  - 97
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DM_2004_16_2_a5/
LA  - ru
ID  - DM_2004_16_2_a5
ER  - 
%0 Journal Article
%A V. B. Alekseev
%T On the number closure-type mappings
%J Diskretnaya Matematika
%D 2004
%P 85-97
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/DM_2004_16_2_a5/
%G ru
%F DM_2004_16_2_a5

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

In this paper, we consider mappings of Cartesian powers $S^n$ of an arbitrary partially ordered set $S$ into itself which possess the main properties of closures. For each partially ordered set, we describe the asymptotic behaviour of the logarithm of the number of such mappings as $n\to\infty$.This research was supported by the Russian Foundation for Basic Research, grant 03–01–00783.

[1] Alekseev V. B., “O chisle semeistv podmnozhestv, zamknutykh otnositelno peresecheniya”, Diskretnaya matematika, 1:2 (1989), 129–136 | MR | Zbl

[2] Alekseev V. B., “O chisle monotonnykh $k$-znachnykh funktsii”, Problemy kibern., 28 (1974), 5–24 | MR | Zbl

[3] Alekseev V. B., Matem. voprosy kibern., 8 (1999), 123–134 | MR | Zbl

[4] Voronenko A. A., “O kolichestve mnogomernykh monotonnykh ekstensivnykh otobrazhenii”, Vestnik Mosk. un-ta. Ser. Vychislitelnaya matem. i kibern., 2001, no. 1, 37–40 | MR | Zbl

[5] Voronenko A. A., “O kolichestve zamknutykh ekstensivnykh otobrazhenii”, Vestnik Mosk. un-ta. Ser. Vychislitelnaya matem. i kibern., 2001, no. 4, 46–48 | MR | Zbl

[6] Voronenko A. A., “O kolichestve zamknutykh mnogomernykh monotonnykh otobrazhenii”, Vestnik Mosk. un-ta. Ser. Vychislitelnaya matem. i kibern., 2002, no. 2, 41–45 | MR | Zbl