Mosaics for immersed surface-links

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 x 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 surfacelinks. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.