The Lattice of Permutations is Bounded

Abstract

The purpose of this paper is to show that the lattice Sn of permutations on a n-element set is bounded. This result strengthens the semi-distributive nature of the lattice Sn. To prove this property, we use a characterization of the class of bounded lattices in terms of arrows relations defined on the join-irreductible elements of a lattice or, more precisely, in terms of the A-table of a lattice.MATHEMATICS