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arXiv · 2303.00699

An open problem on congruences of finite lattices

George Grätzer
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Abstract

Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$. In 2016, I proved a property of congruences of SPS lattices (Two-cover Property) and raised the problem of characterizing them. Since then, more than 50 papers have been published contributing to this problem. In this survey, I provide an overview of this field with major contributions by G\'abor Cz\'edli.

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George Grätzer. 2023-03-01. An open problem on congruences of finite lattices. https://arxiv.org/abs/2303.00699

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