Knot Mosaics for the 10_3 Knot
For many knots, the tile number and/or crossing number cannot be realized when the mosaic number is realized.
The mosaic of the 103 knot given in the table has the mosaic number and tile number realized, but the crossing number of this knot cannot be realized on a 6-mosaic. The crossing number is first realized on a 7-mosaic with 34 non-blank tiles. Below are the relevant mosaics.
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.