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Tile number and space-efficient knot mosaics

Aaron Heap

http://orcid.org/0000-0001-7979-4664

Department of Mathematics, State University of New York at Geneseo, 1 College Circle, Geneseo, NY 14454, USA

E-mail Address: heap@geneseo.edu

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and

Douglas Knowles

Department of Mathematics, Dartmouth College, 27 N. Main Street, Hanover, NH 03755, USA

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https://doi.org/10.1142/S0218216518500414Cited by:4 (Source: Crossref)

Abstract

In this paper, we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot. This least number is called the tile number of the knot. We determine strict bounds for the tile number of a knot in terms of the mosaic number of the knot. We also determine the tile number of several knots and provide space-efficient knot mosaics for each of them.

Keywords:

AMSC: 57M25, 57M27

References

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