Detropicalization as a proof technique

Darij Grinberg; Tom Roby

doi:10.48550/arxiv.2605.30511

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Detropicalization as a proof technique

Darij Grinberg and Tom Roby

ArXiv.org

28 May 2026

DOI: https://doi.org/10.48550/arxiv.2605.30511

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Abstract

Mathematics - Combinatorics

Rational functions make sense over any commutative ring, as long as the denominators are invertible. When there is no subtraction involved, they even apply over semirings (rings without subtraction). It is particularly worthwhile to evaluate them over the *tropical semiring*, in which the roles of addition and multiplication are played by maxima and addition. Over this semiring, algebraic results often acquire combinatorial meaning. We give a few examples.

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Title: Detropicalization as a proof technique
Creators: Darij Grinberg
Tom Roby
Publication Details: ArXiv.org
Resource Type: Preprint
Language: English
Academic Unit: Mathematics
Other Identifier: 991022185876104721

Detropicalization as a proof technique

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