边长小于 1001 的正方形不存在完美的蒙德里安分割

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-10-03 DOI:10.1016/j.dam.2024.09.021

Natalia García-Colín , Dimitri Leemans , Mia Müßig , Érika Roldán

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引用次数: 0

摘要

在数学中，将正方形（或矩形）分割成不相等的矩形就是蒙德里安分割。如果所有矩形的面积相同，则称为完美的蒙德里安分割。在本文中，我们提出了一个计算结果，通过这个结果，我们可以肯定在 n≤1000 时，长度为 n 的正方形不存在完美的蒙德里安分割。使用同样的算法，我们还能确定在 n,m≤400 时，n×m 矩形不存在完美的蒙德里安分割。

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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There is no perfect Mondrian partition for squares of side lengths less than 1001

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length

n

square for

n \leq 1000

. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a

n \times m

rectangle for

n, m \leq 400

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.