Applications of the symmetric chain decomposition of the lattice of divisors

Abstract

The symmetric chain decomposition of the lattice of divisors,D N, is applied to prove results about the strict unimodality of the Whitney numbers ofD N, about minimum interval covers for the union of consecutive rank-sets ofD N, and about the distribution of sums of vectors in which each vector can be included several times (an extension of the famous Littlewood-Offord problem)