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51ºÚÁÏÍø

Knot Mosaic Space

Knot Mosaics for the 9_21 Knot

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

The mosaic of the 921 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 27 non-blank tiles. Below are the relevant mosaics.

921Ìý·É¾±³Ù³óÌýmosaic and tile numbersÌý°ù±ð²¹±ô¾±³ú±ð»å
921Ìý·É¾±³Ù³óÌýcrossing numberÌý°ù±ð²¹±ô¾±³ú±ð»å

Back to the Knot Mosaic Table

References:

Heap, A.; Knowles, D.ÌýSpace-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.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.

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