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.

中文翻译：

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格子结的顶点变形

格子结的顶点畸变是一对顶点沿该结的距离与它们在格子中的距离之比的上确界。ℓ1-规范。受 Gromov、Pardon 和 Blair-Campisi-Taylor-Tomova 的启发，我们证明了平滑结的畸变结果适用于顶点畸变：格结的顶点畸变只有当它是未结时才为 1，并且晶格最小- 具有任意高失真的棒数结构象。