Space-Efficient Prime Knot 7-Mosaics

TL;DR

This paper extends the study of space-efficient prime knot mosaics to those with mosaic number 7, building on previous work that covered mosaics with number 6 or less.

Contribution

It provides new results on tile numbers and space-efficient layouts specifically for prime knots with mosaic number 7.

Findings

Determined tile numbers for prime knots with mosaic number 7.

Identified space-efficient layouts for these knots.

Extended previous classifications to higher mosaic numbers.

Abstract

The concepts of tile number and space-efficiency for knot mosaics were first explored by Heap and Knowles (arXiv:1702.06462), where they determined the possible tile numbers and space-efficient layouts for every prime knot with mosaic number 6 or less. In this paper, we extend those results to prime knots with mosaic number 7.