Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices

2023/01/01 by Gábor Czédli, Czédli, Gábor
Computer Science · #06C10 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2301.00401

openalex publication_date 2023/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following G. Grätzer and E. Knapp (2007), a slim semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no M₃ as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset P is said to be JConSPS-representable if there is an SPS lattice L such that P is isomorphic to the poset J(Con L) of join-irreducible congruences of L. We prove that if 1

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