Work

Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13

Year: 2025

Type: article

Abstract: We give a list of minimal grid diagrams of the 13 crossing prime non-alternating knots which have arc index 13. There are 9,988 prime knots with crossing number 13. Among them 4,878 are alternating and have arc index 15. Among the other non-alternating knots, 49, 399, 1,412, and 3,250 have arc index 10, 11, 12, and 13, respectively. We used the Dowker–Thistlethwaite code of the 3,250 knots provided by the program Knotscape to generate spanning trees of the corresponding knot diagrams to obtain minimal arc presentations in the form of grid diagrams.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500099

Authors: Hwa Jeong Lee, Yoonsang Lee, Chanmin Lee, Yeseo Park, Hun Kim, Gyo Taek Jin

Institutions: Dongguk University WISE, Korea Advanced Institute of Science and Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Award: G432931528