Knots with Exactly 10 Sticks

TL;DR

This paper establishes the exact stick number as 10 for two specific complex knots, marking a significant advancement in understanding the minimal stick representations of non-torus prime knots with high crossings.

Contribution

It provides the first precise stick number determination for non-torus prime knots with more than 9 crossings.

Findings

Knots 13n_{592} and 15n_{41,127} have stick number 10.

First known exact stick numbers for these complex knots.

Advances the understanding of minimal stick representations in knot theory.

Abstract

We prove that the knots $13n_{592}$ and $15n_{41,127}$ both have stick number 10. These are the first non-torus prime knots with more than 9 crossings for which the exact stick number is known.