Lattice stick number 15 is unattainable for non-splittable links

IF 2.6 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica Scripta Pub Date : 2024-09-10 DOI:10.1088/1402-4896/ad6fdf

Youngsik Huh, Sungjong No and Seungsang Oh

引用次数: 0

Abstract

In this paper, we explore mathematical links, defined as closed curves embedded in 3D space. Knot theory studies these structures, which also occur in real-world biopolymers like DNA. Lattice links are links in the cubic lattice. For scientific simulations or statistical studies, links are simplified to lattice links. The lattice stick number, denoted as sL(K), is the minimum number of lattice sticks needed to represent a link K in the cubic lattice. In previous study, it was shown that only two non-trivial knots and six non-splittable links have sL ≤ 14: specifically, , = , , and . Recent study has further revealed that no knot can have sL = 15. In this paper, we prove that lattice stick number 15 is not attainable for non-splittable links. As a corollary, eleven non-splittable links with sL=16 are presented.

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对于不可拆分链路来说，网格棍数 15 是无法实现的

在本文中，我们探讨了数学链接，其定义为嵌入三维空间的封闭曲线。结理论研究这些结构，它们也出现在现实世界的生物聚合物（如 DNA）中。晶格链接是立方晶格中的链接。在科学模拟或统计研究中，链接被简化为晶格链接。晶格棒数表示为 sL(K)，是表示立方晶格中的链接 K 所需的最小晶格棒数。之前的研究表明，只有两个非难结和六个不可拆分链接的 sL ≤ 14：特别是， = ，和。最近的研究进一步发现，没有一个结的 sL = 15。在本文中，我们证明了不可拆分链接不可能达到网格棍数 15。作为推论，本文提出了 11 个 sL=16 的不可拆分链接。

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

Physica Scripta 物理-物理：综合

CiteScore

3.70

自引率

3.40%

发文量

782

审稿时长

4.5 months

期刊介绍： Physica Scripta is an international journal for original research in any branch of experimental and theoretical physics. Articles will be considered in any of the following topics, and interdisciplinary topics involving physics are also welcomed: -Atomic, molecular and optical physics- Plasma physics- Condensed matter physics- Mathematical physics- Astrophysics- High energy physics- Nuclear physics- Nonlinear physics. The journal aims to increase the visibility and accessibility of research to the wider physical sciences community. Articles on topics of broad interest are encouraged and submissions in more specialist fields should endeavour to include reference to the wider context of their research in the introduction.