Minimum volumes of tropical rational functions
Abstract
When a tropical rational function on Rn is given, we can represent it as =f-g with tropical polynomials f and g. We develop the duality theorem for tropical rational functions to define the volume of the pair (f, g). We show that when n=1, we can find a representation of (x) ≠ -∞ as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) (yg(x)) is unique up to translation, but when n=2 this is not true.
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