  Let $\{h_1,h_2,...\}$ be a set of algebraically independent variables. We ask
which vectors are extreme in the cone generated by $h_ih_j-h_{i+1}h_{j-1}$
($i\geq j>0$) and $h_i$ ($i>0$). We call this cone the cone of log concavity.
More generally, we ask which vectors are extreme in the cone generated by Schur
functions of partitions with $k$ or fewer parts. We give a conjecture for which
vectors are extreme in the cone of log concavity. We prove the characterization
in one direction and give partial results in the other direction.
