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

Yueheng Bao; Ari Benveniste; Marion Campisi; Nicholas Cazet; Ansel Goh; Jiantong Liu; Ethan Sherman

doi:10.1142/s0218216523500979

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arXiv · 2211.00687

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

Yueheng Bao·Ari Benveniste·Marion Campisi·Nicholas Cazet·Ansel Goh·Jiantong Liu·Ethan Sherman

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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 ($3_1$) and the figure-eight knot ($4_1$).

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BibTeX RIS

Yueheng Bao, Ari Benveniste, Marion Campisi, Nicholas Cazet, Ansel Goh, Jiantong Liu, Ethan Sherman. 2022-11-01. Bounds in simple hexagonal lattice and classification of 11-stick knots. https://doi.org/10.1142/s0218216523500979

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