THE LATTICE OF PERMUTATIONS IS BOUNDED

Abstract

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