Quandle - Definition and Overview

In mathematics, a rack and a quandle in knot theory are sets with a binary operation mimicking the three Reidemeister moves of diagram manipulation.

Suppose that the binary operation is written <math>a*b<math>. Then the three laws for a quandle are

1. <math>a*a=a<math>
2. <math>x\to x*a<math> is a bijection for all <math>a<math>
3. <math>(a*b)*c=(a*c)*(b*c)<math>

A rack is more general than a quandle: it satisfies only the two last laws.

An alternative definition of a rack is that it is a set with a binary operation in which multiplication on one side is an automorphism.