Abstract. Slim rectangular lattices were introduced by G. Grätzer and E. Knapp in Acta Sci. Math. 75, 29--48, 2009. They are finite semimodular lattices $L$ such that the poset $\jir L$ of join-irreducible elements of $L$ is the cardinal sum of two nontrivial chains. Using deep tools and involved considerations, a 2013 paper by G. Czédli and the present authors proved that a slim semimodular lattice is rectangular iff so is the Jordan--Hölder permutation associated with it. Here, we give an easier and more elementary proof.

DOI: 10.14232/actasm-015-271-y

AMS Subject Classification (1991): 06C10

Keyword(s): rectangular lattice, semimodularity, slim lattice, planar lattice, combinatorics of permutations

Received June 26, 2014, and in revised form March 2, 2015. (Registered under 21/2015.)