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

Publication Date

12-1-2023

Document Type

Article

Publication Title

Journal of Knot Theory and its Ramifications

Volume

32

Issue

14

DOI

10.1142/S0218216523500979

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 11-stick knots in the sh-lattice are the trefoil knot (31) and the figure-eight knot (41).

Keywords

lattice knot, Polygonal knot, simple hexagonal lattice, stick number

Department

Mathematics and Statistics

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