Families of not perfectly straight knots

TL;DR

This paper introduces two new families of knots with higher straight numbers than crossing numbers, computes the straight number for one family, and proves a theorem about the effect of adding crossings to twist regions in alternating knots.

Contribution

It presents two novel knot families with higher straight numbers and a theorem on how adding crossings affects knot straightness.

Findings

Computed the straight number explicitly for one knot family.

Proved adding even crossings to a twist region does not change knot straightness.

Identified families of knots with higher straight numbers than crossing numbers.

Abstract

We present two families of knots which have straight number higher than crossing number. In the case of the second family, we have computed the straight number explicitly. We also give a general theorem about alternating knots that states adding an even number of crossings to a twist region will not change whether the knots are perfectly straight or not perfectly straight.