Petal number of torus knots of type $(r,r+2)$

TL;DR

This paper determines the petal number of torus knots of type (r, r+2) for odd r, showing it equals 2r+3, thus providing a precise measure of their complexity.

Contribution

It establishes an exact formula for the petal number of (r, r+2) torus knots when r is odd, filling a gap in knot complexity measurements.

Findings

Petal number of (r, r+2) torus knots is 2r+3 for odd r.

Provides a closed-form formula for a specific class of torus knots.

Enhances understanding of knot complexity metrics.

Abstract

Let $r$ be an odd integer, $r\ge3$. Then the petal number of the torus knot of type $(r,r+2)$ is equal to $2r+3$.