2023/08/30 by Seonmi Choi, Choi, Seonmi, Jieon Kim +1
Computer Science · Mathematics · #57K12 #57K45 #81P99 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2308.15737
openalex publication_date 2023/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The concept of a knot mosaic was introduced by Lomonaco and Kauffman as a means to construct a quantum knot system. The mosaic number of a given knot K is defined as the minimum integer n that allows the representation of K on an n × n mosaic board. Building upon this, the first author and Nelson extended the knot mosaic system to encompass surface-links through the utilization of marked graph diagrams and established both lower and upper bounds for the mosaic number of the surface-links presented in Yoshikawa's table. In this paper, we establish a mosaic system for immersed surface-links by using singular marked graph diagrams. We also provide the definition and discussion on the mosaic number for immersed surface-links.