Geodesic
The structure of finite distributive lattices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 2, pp. 219-226 
V. D. Shmatkov. The structure of finite distributive lattices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 2, pp. 219-226. http://geodesic.mathdoc.fr/item/FPM_2014_19_2_a12/
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     title = {The structure of finite distributive lattices},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to the structure that describes the construction of finite distributive lattices. From the viewpoint of application, we consider algorithms of construction and enumeration of distributive lattices and partially ordered sets for finite distributive lattices: a formula for finding the maximum anti-chain with respect to nonintersection is given, it is shown that elements of the lattice can be split into pairs according to comparison, we consider the point of the maximum number of elements in the lattices, and the structure of lattice congruence is described.

[1] Birkgof G., Teoriya reshëtok, Nauka, M., 1984 | MR

[2] Grettser G., Obschaya teoriya reshëtok, Mir, M., 1982 | MR

[3] Marenich E. E., “Perechislenie reshenii nekotorykh uravnenii v konechnykh reshëtkakh”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1997, no. 3, 16–21 | MR | Zbl

[4] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990 | MR

[5] Erdős P., Herzog M., Schönheim J., “An extremal problem on the set of noncoprime divisors of a number”, Israel J. Math., 408:4 (1970), 408–412 | MR | Zbl