The Structure of Finite Distributive Lattices

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• 作者：V. D. Shmatkov
• 刊名：Journal of Mathematical Sciences
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：213
• 期：2
• 页码：276-280
• 全文大小：138 KB
• 参考文献：1.G. Birkhoff, Theory of Lattices [Russian translation], Nauka, Moscow (1984).
  2.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.
  3.G. Grätzer, General Lattice Theory [Russian translation], Mir, Moscow (1982).
  4.E. E. Marenich, “Enumerative solutions of certain equations in finite lattices,” Vestn. Mosk. Univ. Ser. 1 Mat., Mekh., No. 3, 16–21 (1997).
  5.R. P. Stanley, Enumerative Combinatorics [Russian translation], Mir, Moscow (1990).
  
• 作者单位：V. D. Shmatkov (1)
  
  1. Ryazan State Radio Engineering University, Ryazan, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8795

文摘

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. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 2, pp. 219–226, 2014.