Minimal solutions of tropical linear differential systems

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2026-03-30 DOI:10.1007/s00200-025-00722-5

Dima Grigoriev, Cristhian Garay López

引用次数: 0

Abstract

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.

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热带线性微分系统的极小解

介绍并研究了热带线性微分方程有限系统的最小解（相对于包含）。我们描述了单个方程所有最小解的集合。证明了任一热带线性微分方程在单未知数下要么有解，要么在无穷远处有解。对于一类具有相同未知量的n个热带线性微分方程的一般系统，建立了最小解个数的上界和下界。上界涉及置换族的反转，它推广了单个置换的反转。对于\(n=1, 2\)，我们证明了边界是清晰的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.