Abstract
In 2008, Kauffman and Lomonaco introduced the concepts of a knot mosaic and the mosaic number of a knot or link , the smallest integer such that can be represented on an -mosaic. In 2018, the authors of this paper introduced and explored space-efficient knot mosaics and the tile number of , the smallest number of nonblank tiles necessary to depict on a knot mosaic. They determine bounds for the tile number in terms of the mosaic number. In this paper, we focus specifically on prime knots with mosaic number 6. We determine a complete list of these knots, provide a minimal, space-efficient knot mosaic for each of them, and determine the tile number (or minimal mosaic tile number) of each of them.
Citation
Aaron Heap. Douglas Knowles. "Space-efficient knot mosaics for prime knots with mosaic number 6." Involve 12 (5) 767 - 789, 2019. https://doi.org/10.2140/involve.2019.12.767
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