Bounds in simple hexagonal lattice and classification of 11-stick knots-Reference-Cited by-同舟云学术

Bounds in simple hexagonal lattice and classification of 11-stick knots

Published:2023-12 Issue:14 Volume:32 Page:
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Bao Yueheng¹^ORCID,Benveniste Ari²^ORCID,Campisi Marion³^ORCID,Cazet Nicholas⁴^ORCID,Goh Ansel⁵^ORCID,Liu Jiantong⁶^ORCID,Sherman Ethan⁷^ORCID

Affiliation:

1. University of Science and Technology of China, Hefei, Anhui, China

2. Pomona College, Claremont CA, USA

3. San Jose State University, San Jose, CA, USA

4. University of California, Davis, CA, USA

5. University of Washington, Seattle, WA, USA

6. University of California, Los Angeles, CA, USA

7. Vanderbilt University, Nashville, Tennessee, USA

Abstract

The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a knot of the given type in sh-lattice. By introducing a linear transformation between lattices, we prove that for any given knot both values in the sh-lattice are strictly less than the values in the cubic lattice. Finally, we show that the only non-trivial [Formula: see text]-stick knots in the sh-lattice are the trefoil knot ([Formula: see text]) and the figure-eight knot ([Formula: see text]).

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216523500979

Reference8 articles.

1. STICK INDEX OF KNOTS AND LINKS IN THE CUBIC LATTICE

2. Stick numbers in the simple hexagonal lattice

3. The number of smallest knots on the cubic lattice

4. Lattice stick number of knots

5. LATTICE STICK NUMBERS OF SMALL KNOTS