Lattice stick number 15 is unattainable for non-splittable links
Year: 2024
Type: article
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 s L (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 s L ≤ 14: specifically, s L ( 2 1 2 ) = 8 , s L ( 3 1 ) = s L ( 2 1 2 ♯ 2 1 2 ) = s L ( 6 2 3 ) = s L ( 6 3 3 ) = 12 , s L ( 4 1 2 ) = 13 , and s L ( 4 1 ) = s L ( 5 1 2 )
Source: Physica Scripta
Authors: Youngsik Huh, Sungjong No, Seungsang Oh
Institutions: Hanyang University, Kyonggi University, Korea University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,285
Award: G8708098660
OpenAlex ID: W4401598869