# Generating sets of Reidemeister moves of oriented singular links and quandles

## TL;DR

This paper introduces a generating set of Reidemeister moves for oriented singular links, develops a new algebraic structure from singular knots, and demonstrates its effectiveness in distinguishing singular links.

## Contribution

It provides a new generating set for Reidemeister moves and a novel algebraic structure for oriented singular knots, with examples and invariance properties.

## Key findings

- Set of colorings is an invariant of singular knots
- Constructed non-isomorphic structures over non-abelian groups
- Distinguished some singular links using the new invariants

## Abstract

We give a generating set of the generalized Reidemeister moves for oriented singular links. We use it to introduce an algebraic structure arising from the study of oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of colorings of a singular knot by this new structure is an invariant of oriented singular knots and use it to distinguish some singular links.