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math.GMMay 22, 2007
40
citations (OpenAlex)
authors
  • G. Grätzer
  • E. Knapp
arXiv abstractPDF
paper

Notes on planar semimodular lattices. I. Construction

arXiv:0705.3366

Abstract

We construct all planar semimodular lattices in three simple steps from the direct product of two chains.

arXiv comment13 pages with 9 diagrams

Cited by in corpus (7)

  • Notes on planar semimodular lattices. VII. Resections of planar semimodular lattices
  • The asymptotic number of planar, slim, semimodular lattice diagrams
  • A new property of congruence lattices of slim, planar, semimodular lattices
  • Slim patch lattices as absolute retracts and maximal lattices
  • Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices
  • Using the Swing Lemma and C1​-diagrams for congruences of planar semimodular lattices
  • Length-preserving extensions of semimodular lattices by lowering join-irreducible elements
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