Research ArticleNo Access

Vertex distortion of lattice knots

Marion Campisi

https://orcid.org/0000-0002-5735-3099

San José State University, 1 Washington Sq, San Jose, CA 95192, USA

E-mail Address: marion.campisi@sjsu.edu

Corresponding author.

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and

Nicholas Cazet

University of California at Davis, 1 Shields Ave, Davis, CA 95616, USA

E-mail Address: nccazet@ucdavis.edu

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https://doi.org/10.1142/S0218216521500437Cited by:1 (Source: Crossref)

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 $ℓ_{1}$ -norm. Inspired by Gromov, Pardon and Blair–Campisi–Taylor–Tomova, we show that results 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 there are minimal lattice-stick number knot conformations with arbitrarily high distortion.

Keywords:

AMSC: 57K10, 57M50

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