Symmetric and r-symmetric tropical polynomials and rational functions
2016
A tropical polynomial in nr variables, divided into blocks of r variables each, is r-symmetric if it is invariant under the action of Sn 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.
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