The Structure of Finite Distributive Lattices

被引：0

作者：

Shmatkov V.D. ^{[1
]}

机构：

[1] Ryazan State Radio Engineering University, Ryazan

来源：

Journal of Mathematical Sciences | 2016年 / 213卷 / 2期

关键词：

Equivalence Class; Direct Product; Russian Translation; Distributive Lattice; Small Element;

D O I：

10.1007/s10958-016-2717-1

中图分类号：

学科分类号：

摘要：

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. © 2016, Springer Science+Business Media New York.

引用

页码：276 / 280

页数：4

共 5 条

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[2]

Erdos P., Herzog M., Schönheim, “An extremal problem on the set of noncoprime divisors of a number,” Israel J, Math., 408, 4, pp. 408-412

[3]

Gratzer G., General Lattice Theory [Russian translation], (1982)

[4]

Marenich E.E., Enumerative solutions of certain equations in finite lattices,, Vestn. Mosk. Univ. Ser. 1 Mat., Mekh., 3, pp. 16-21, (1997)

[5]

Stanley R.P., Enumerative Combinatorics [Russian translation], (1990)

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