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51ºÚÁÏÍø

Knot Mosaic Space

Knot Mosaics for the 10_13 Knot

For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized.

The mosaic of the 1013 knot given in the table has the mosaic number and tile number realized, but the crossing number of this knot cannot be realized when the tile number (27) is. The crossing number is first realized with 29 non-blank tiles. Below are the relevant mosaics.

1013 with mosaic and tile numbers realized
1013Ìý·É¾±³Ù³óÌýmosaic and tile numbersÌý°ù±ð²¹±ô¾±³ú±ð»å
1013 with crossing number realized
1013Ìý·É¾±³Ù³óÌýcrossing numberÌý°ù±ð²¹±ô¾±³ú±ð»å

Back to the Knot Mosaic Table

References:

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.

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