On positive and almost alternating links

TL;DR

This paper investigates the properties of positive and almost alternating links, proving that such links with positive and almost alternating diagrams are actually alternating, and characterizes certain Montesinos links with almost positive-alternating diagrams.

Contribution

It establishes a new link between positive, almost alternating, and alternating links, and characterizes specific Montesinos links with almost positive-alternating diagrams.

Findings

Positive and almost alternating diagrams imply the link is alternating.

Positive, non-alternating Montesinos links have almost positive-alternating diagrams.

Provides criteria for classifying Montesinos links based on their diagrams.

Abstract

In this paper, we show that a link which has a positive and almost alternating diagram is alternating, besides that a positive and non-alternating Montesinos link has an almost positive-alternating diagram.