Bounding Crossing Number in Rectangular and Hexagonal Knot Mosaics

2024/10/25 by Hugh Howards, Jiong Li, Howards, Hugh +3
Computer Science · Engineering · #Digital Image Processing Techniques #Computational Geometry and Mesh Generation #3D Shape Modeling and Analysis

paper · pdf · doi:10.48550/arxiv.2410.19570

Abstract

Howards and Kobin give a sharp upper bound for crossing number of knots on rectangular mosaics. Here we extend the proof to create a new bound for hexagonal mosaics in all three natural settings and shorten the proof in the rectangular setting.

Related

• Bounds on Mosaic Knots
• Crossing Number Bound in Knot Mosaics
• An infinite family of knots whose hexagonal mosaic number is only realized in non-reduced projections
• Mosaic number of knots
• Mosaic number and Tile number of Corner Connection Tiles