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2019 Space-efficient knot mosaics for prime knots with mosaic number 6
Aaron Heap, Douglas Knowles
Involve 12(5): 767-789 (2019). DOI: 10.2140/involve.2019.12.767

Abstract

In 2008, Kauffman and Lomonaco introduced the concepts of a knot mosaic and the mosaic number of a knot or link K, the smallest integer n such that K can be represented on an n-mosaic. In 2018, the authors of this paper introduced and explored space-efficient knot mosaics and the tile number of K, the smallest number of nonblank tiles necessary to depict K 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

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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

Information

Received: 28 March 2018; Revised: 4 October 2018; Accepted: 27 December 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07072553
MathSciNet: MR3954295
Digital Object Identifier: 10.2140/involve.2019.12.767

Subjects:
Primary: 57M25
Secondary: 57M27

Keywords: crossing number , knot mosaic , knots , mosaic number , space-efficient , tile number

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 5 • 2019
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