2017/03/15 by Kyungpyo Hong, Hong, Kyungpyo, Seungsang Oh +1
Computer Science · Mathematics · #05C30 #57M25 #81P99 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1703.04868
openalex publication_date 2017/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is intended to represent an actual physical quantum system. Recently the authors developed an algorithm producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. As a sequel to this research program, we similarly define the (embedded) graph mosaic system by using sixteen graph mosaic tiles, representing graph diagrams with vertices of valence 3 and 4. And we extend the algorithm to produce the exact number of all graph mosaics. The magnified state matrix that is an extension of the state matrix is mainly used.