Scholarlink

<p>We introduce and study minimal (with respect to inclusion) solutions of finite 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 <i>n</i> tropical linear differential equations in the same number of 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n=1, 2\)</EquationSource> </InlineEquation>, we show that the bounds are sharp.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Minimal solutions of tropical linear differential systems

  • 期刊论文

  • 发表日期：

    2026年3月30日

查看全文
  • Dima Grigoriev,
  • Cristhian Garay López

摘要

We introduce and study minimal (with respect to inclusion) solutions of finite 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 the same number of 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.