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arXiv · 2503.23703

Minimal solutions of tropical linear differential systems

Dima Grigoriev·Cristhian Garay López
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Abstract

We introduce and study minimal (with respect to inclusion) solutions of systems of tropical linear differential equations. We describe the set of all minimal solutions for a single equation. It is shown that any tropical linear differential equation in a single unknown has either a solution or a solution at infinity. For a generic system of $n$ tropical linear differential equations in $n$ unknowns, upper and lower bounds on the number of minimal solutions are established. The upper bound involves inversions of a family of permutations which generalize inversions of a single permutation. For $n=1, 2$, we show that the bounds are sharp.

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Dima Grigoriev, Cristhian Garay López. 2025-03-31. Minimal solutions of tropical linear differential systems. https://arxiv.org/abs/2503.23703

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