Symmetric and r-symmetric tropical polynomials and rational functions.

A tropical polynomial in nr variables, divided into blocks of r variables each, is r -symmetric if it is invariant under the action of S n that permutes the blocks. For r = 1 we call these symmetric tropical polynomials. We can define r -symmetric and symmetric tropical rational functions in a similar manner. In this paper we identify generators for the sets of symmetric tropical polynomials and rational functions. While r -symmetric tropical polynomials are not finitely generated for r ≥ 2 , we show that r -symmetric tropical rational functions are and provide a list of generators. [ABSTRACT FROM AUTHOR]