A new extension of Lubell's inequality to the lattice of divisors

Abstract

P. L. Erdos and G. O. H. Katona gave an inequality involving binomial coefficients summed over an antichain in the product of two chains. Here we present the common generalization of this inequality and Lubell's famous inequality for the Boolean lattice to an arbitrary product of chains (lattice of divisors). We also describe the connection between this inequality and the LYM property.