Tile number and space-efficient knot mosaics-Reference-Cited by-同舟云学术

Tile number and space-efficient knot mosaics

Published:2018-05 Issue:06 Volume:27 Page:1850041
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Heap Aaron¹^ORCID,Knowles Douglas²

Affiliation:

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216518500414

Reference5 articles.

1. THE LOMONACO–KAUFFMAN CONJECTURE

2. Mosaic number of knots

3. Knot mosaic tabulation

4. Quantum knots and mosaics

5. AN INFINITE FAMILY OF KNOTS WHOSE MOSAIC NUMBER IS REALIZED IN NON-REDUCED PROJECTIONS

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