Almost alternating knots with 12 crossings and Turaev genus

TL;DR

This paper investigates non-alternating knots with up to 12 crossings, demonstrating that most are almost alternating and thus have Turaev genus 1, filling gaps in existing knot classification data.

Contribution

It establishes that 154 previously unclassified non-alternating knots with up to 12 crossings are almost alternating, determining their Turaev genus as 1.

Findings

154 knots shown to be almost alternating

Turaev genus determined as 1 for these knots

Provides new classification data for knots with up to 12 crossings

Abstract

Among non-alternating knots with $n\le 12$ crossings given in \cite{1} Turaev genus is not known for 191 knot. For 154 of them we show that they are almost alternating, so their Turaev genus is 1.