Slim lattice

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In lattice theory, a mathematical discipline, a finite lattice is slim if no three join-irreducible elements form an antichain.[1] Every slim lattice is planar. A finite planar semimodular lattice is slim if and only if it contains no cover-preserving diamond sublattice M3 (this is the original definition of a slim lattice due to George Grätzer and Edward Knapp).[2]

Notes

  1. (Czédli Schmidt)
  2. (Grätzer Knapp)

References