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arXiv · 2409.18348

Minimum volumes of tropical rational functions

Masayuki Sukenaga
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Abstract

When a tropical rational function \varphi on R^n is given, we can represent it as \varphi=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 \varphi(x) \neq -\infty as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) \oplus (yg(x)) is unique up to translation, but when n=2 this is not true.

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Masayuki Sukenaga. 2024-09-26. Minimum volumes of tropical rational functions. https://arxiv.org/abs/2409.18348

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