Vertex distortion of lattice knots
Journal of Knot Theory and its Ramifications
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. 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.
distortion, Lattice knots
Mathematics and Statistics
Marion Campisi and Nicholas Cazet. "Vertex distortion of lattice knots" Journal of Knot Theory and its Ramifications (2021). https://doi.org/10.1142/S0218216521500437