Abstract
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, the point of the maximum number of elements in the lattices is considered, and the structure of lattice congruence is described.
Similar content being viewed by others
References
G. Birkhoff, Theory of Lattices [Russian translation], Nauka, Moscow (1984).
P. Erdős, M. Herzog, and J. Schönheim, “An extremal problem on the set of noncoprime divisors of a number,” Israel J. Math., 408, No. 4, 408–412.
G. Grätzer, General Lattice Theory [Russian translation], Mir, Moscow (1982).
E. E. Marenich, “Enumerative solutions of certain equations in finite lattices,” Vestn. Mosk. Univ. Ser. 1 Mat., Mekh., No. 3, 16–21 (1997).
R. P. Stanley, Enumerative Combinatorics [Russian translation], Mir, Moscow (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 2, pp. 219–226, 2014.
Rights and permissions
About this article
Cite this article
Shmatkov, V.D. The Structure of Finite Distributive Lattices. J Math Sci 213, 276–280 (2016). https://doi.org/10.1007/s10958-016-2717-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-016-2717-1