The asymptotic behavior of elementary symmetric functions on a probability distribution

Abstract

The problem on asymptotic of the value π(m,n)=m!σm(p(1,n),p(2,n),…,p(n,n)) is considered, where σm(x1,x2,…,xn) is the mth elementary symmetric function of n variables. The result is interpreted in the context of nonequiprobable random mappings theory