APPLICATIONS OF THE SYMMETRICAL CHAIN DECOMPOSITION OF THE LATTICE OF DIVISORS

The symmetric chain decomposition of the lattice of divisors, D(N), is applied to prove results about the strict unimodality of the Whitney numbers of D(N), about minimum interval covers for the union of consecutive rank-sets of D(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).