Space-Efficient Prime Knot 7-Mosaics
Aaron Heap, Natalie LaCourt

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
