A characterization for all interval doubling schemes of the lattice of permutations

Abstract

The lattice S n of all permutations on a n-element set has been shown to be bounded [CAS], which is a strong constructive property characterized by the fact that S n admits what we call an interval doubling scheme. In this paper we characterize all interval doubling schemes of the lattice S n, a result that gives a nice precision on the bounded nature of the lattice of permutations. This theorem is a direct corollary of two strong properties that are also given with their proofs.