{"title":"Lattice stick number 15 is unattainable for non-splittable links","authors":"Youngsik Huh, Sungjong No and Seungsang Oh","doi":"10.1088/1402-4896/ad6fdf","DOIUrl":null,"url":null,"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.","PeriodicalId":20067,"journal":{"name":"Physica Scripta","volume":"24 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica Scripta","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1402-4896/ad6fdf","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.
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