A note on the unknotting number and the region unknotting number of weaving knots

TL;DR

This paper introduces the warping degree for braid diagrams and uses it to establish upper bounds on the unknotting and region unknotting numbers for certain weaving knots through diagrammatic and combinatorial analysis.

Contribution

It defines the warping degree for braid diagrams and provides new upper bounds for unknotting and region unknotting numbers of weaving knots.

Findings

Upper bounds for unknotting numbers of weaving knots

Upper bounds for region unknotting numbers of weaving knots

Introduction of warping degree as a tool for analysis

Abstract

A weaving knot is an alternating knot whose minimal diagram is a closed braid of a lattice-like pattern. In this paper, the warping degree of a braid diagram is defined, and upper bounds of the unknotting number and the region unknotting number for some families of weaving knots are given by diagrammatical and combinatorial examination of the warping degree of weaving knot diagrams.