Superdominance order and symmetric function inequalities

We classify all pure binomial inequalities among power sum symmetric functions that hold on the nonnegative orthant in any number of variables. When restricted to positive integer exponents, these valid inequalities are completely characterized by the superdominance order on partitions. We use polyhedral geometry and tropical convexity to obtain these results.

In addition, we study and compare the cones of symmetric functions that are nonnegative and those that are sums of squares in any number of variables.

This is joint work with Jose Acevedo, Greg Blekherman, and Cordian Riener.