2021/04/28 by George Grätzer, G. Grätzer, Grätzer, G.
Computer Science · Mathematics · #06B05 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Rings and Algebras (math.RA) #math.CO #math.RA #msc:06B05 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2104.13532
arxiv created 2021/04/28 · openalex publication_date 2021/04/28 · arxiv updated 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we discuss planar lattices generated by their atoms. We prove that if L is a planar lattice generated by n atoms, then both the left and the right boundaries of L have at most n+1 elements. On the other hand, L can be arbitrarily large. For every k > 1, we construct a planar lattice L generated by 4 atoms such that L has more than k elements.