Conjectured upper bound for the mosaic number of a knot

Let KK be a knot with crossing number cc, and let nn be its mosaic number.

Mosaic-number upper-bound conjecture. The mosaic number satisfies

nc+2.n\leq c+2.

This conjecture is motivated by experimental evidence and proposes a sharper upper bound than the preceding general bound n4c+2n\leq 4c+2.

Sources & referencesView supporting material

Primary source

J. Alan Alewine, H. A. Dye, David Etheridge, Irina Garduno and Amber Ramos, “Bounds on Mosaic Knots”, arXiv:1004.2214 (2010).

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