Log concave sequences of symmetric functions and analogs of the Jacobi-Trudi determinants

Abstract

We prove that various sequences of elementary and complete homogeneous symmetric functions are log concave or PF. As corollaries we show that certain sequences of q q -binomial coefficients and q q -Stirling numbers have these properties. The principal technique used is a combinatorial interpretation of determinants using lattice paths due to Gessel and Viennot [G-V 85].