DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

G. Grätzer

George Grätzer

Department of Mathematics
University of Manitoba
Winnipeg, MB R3T 2N2, Canada

email: gratzer@me.com

Title:

Notes on planar semimodular lattices IX $\boldsymbol{\mathcal{C}_1}$-diagrams

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 25-29

Received: 2021-05-05 , Revised: 2021-05-30 , Accepted: 2021-05-30 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1409

Abstract:

A planar semimodular lattice $L$ is slim if $\mathsf M_3$ is not a sublattice of $L$. In a recent paper, G. Czédli introduced a very powerful diagram type for slim, planar, semimodular lattices, the $\mathcal{C}_1$-diagrams. This short note proves the existence of such diagrams.

Keywords:

$\mathcal{C}_1$-diagrams, slim planar semimodular lattice

References:

  1. G. Czédli, Patch extensions and trajectory colorings of slim rectangular lattices, Algebra Universalis 72 (2014) 125–154.
    https://doi.org/10.1007/s00012-014-0294-z
  2. G. Czédli, A note on congruence lattices of slim semimodular lattices, Algebra Universalis 72 (2014) 225–230.
    https://doi.org/10.1007/s00012-014-0286-z
  3. G. Czédli, Diagrams and rectangular extensions of planar semimodular lattices, Algebra Universalis 77 (2017) 443–498.
    https://doi.org/10.1007/s00012-017-0437-0
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    https://doi.org/10.1007/s00012-020-0641-1
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