Affiliations: [a] College of Applied Mathematics, Chengdu University of Information Technology Chengdu, Sichuan People’s Republic of China | [b] School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People’s Republic of China
Correspondence:
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Corresponding author. Peng He, College of Applied Mathematics, Chengdu University of Information Technology Chengdu, Sichuan 610225, People’s Republic of China. E-mail: hepeng@cuit.edu.cn
Note: [1] Supported by National Natural Science Foundation of China (Nos. 11171242 and 11901064).
Abstract: Let D be a finite distributive lattice with n join-irreducible elements. It is well-known that D can be represented as the congruence lattice of a rectangular lattice L which is a special planer semimodular lattice. In this paper, we shall give a better upper bound for the size of L by a function of n, improving a 2009 result of G. Grätzer and E. Knapp.
