Knot Mosaics for the 10_34 Knot

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

The mosaic of the 1034 knot given in the table has the mosaic number (6) and tile number (27) realized, but the crossing number of this knot cannot be realized with only 27 non-blank tiles. The crossing number is first realized on a 6-mosaic with 32 non-blank tiles, but it can also be realized on a 7-mosaic with 29 non-blank tiles. Below are the relevant mosaics.
1034 with mosaic and tile numbers realized
1034 with crossing number realized on a 6-mosaic with 32 non-blank tiles
1034 with crossing number realized on a 7-mosaic with 29 non-blank tiles

Back to the Knot Mosaic Table

References:

Heap, A.; Knowles, D. Space-Efficient Knot Mosaics for Prime Knots with Mosaic Number 6; Involve 2019, 12.

Heap, A.; Baldwin, D.; Canning, J.; Vinal, G. Tabulating Knot Mosaics: Crossing Number 10 or Less; in preparation.