Quandle (knot theory)

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 a * b. Then the three laws for a quandle are

1. a * a = a
2. is a bijection for all a
3. (a * b) * c = (a * c) * (b * c)

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.