Table of Knot Mosaics – Crossing number 10 or less
- Return to Knot Mosaic Space
- Crossing number 10 or less
- Mosaic number 5 or less
- Mosaic number 6 or less
- Mosaic number 7 or less (Coming soon)
The mosaics in this table are color coded with the following key (t = tile number, tm = minimal mosaic tile number):
- Mosaic number 5:
: t = 17; - Mosaic number 6: : t = 22; : t = 24; : t = 27; : tm = 32*;
- Mosaic number 7: : t = 27; : t = 29; : t = 31
: t = 17;
: t = 22; 
: t = 24; 
: t = 27; 
: tm = 32*;
: t = 27; 
: t = 29; 
: t = 31* Note: Prime knots that require 32 non-blank tiles to fit on a 6-mosaic (i.e. tm = 32) may have tile number less than 32 that can only be achieved on a 7-mosaic. All given mosaics have mosaic number realized. Click 渕ore� to see mosaics with tile number or crossing number realized.
Click mosaic for larger view.
References:
Heap, A.; Knowles, D. Tile Number and Space-Efficient Knot Mosaics; J. Knot Theory Ramif. 2018, 27.
Heap, A.; Knowles, D. Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6; Involve 2019, 12.
Heap, A.; LaCourt, N. Space-Efficient Prime Knot 7-Mosaics; Symmetry 2020, 12.
Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Tabulating Knot Mosaics: Crossing Number 10 or Less; in preparation.
Kuriya, T.; Shehab, O. The Lomonaco揔auffman Conjecture; J. Knot Theory Ramif. 2014, 23.
Lee, H.; Ludwig, L.; Paat, J.; Peiffer, A. Knot Mosaic Tabulation; Involve 2018, 11.
Lomonaco, S.J.; Kauffman, L.H. Quantum Knots and Mosaics; Quantum Inf. Process. 2008, 7, 85�115.
Ludwig, L.; Evans, E. An Infinite Family of Knots Whose Mosaic Number Is Realized in Non-reduce Projections; J. Knot Theory Ramif. 2013, 22.
Rolfsen, D. Knots and Links; Publish or Perish Press: Berkeley, CA, USA, 1976.