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- Title
Bounds in simple hexagonal lattice and classification of 11-stick knots.
- Authors
Bao, Yueheng; Benveniste, Ari; Campisi, Marion; Cazet, Nicholas; Goh, Ansel; Liu, Jiantong; Sherman, Ethan
- 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 1 1 -stick knots in the sh-lattice are the trefoil knot ( 3 1 ) and the figure-eight knot ( 4 1 ).
- Subjects
KNOT theory; CLASSIFICATION
- Publication
Journal of Knot Theory & Its Ramifications, 2023, Vol 32, Issue 14, p1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216523500979