Vertex distortion of lattice knots

Marion Campisi; Nicholas Cazet

doi:10.1142/s0218216521500437

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arXiv · 2009.03502

Vertex distortion of lattice knots

Marion Campisi·Nicholas Cazet

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Abstract

The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous results to those of Gromov, Pardon and Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for vertex distortion: the vertex distortion of a lattice knot is 1 only if it is the unknot, and that there are minimal lattice-stick number knot conformations with arbitrarily high distortion.

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Marion Campisi, Nicholas Cazet. 2020-09-08. Vertex distortion of lattice knots. https://doi.org/10.1142/s0218216521500437

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