Table of Knot Mosaics - Crossing number 10 or less
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The mosaics in this table are color coded with the following key (t = tile number, tm = minimal mosaic tile number):
* 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 "more" to see mosaics with tile number or crossing number realized. |
Click mosaic for larger view.
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*These knots are listed as 10162‑10166 in Rolfsen due to the Perko Pair. | |||||
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–Kauffman 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.