Biracks and biquandles

Biracks and biquandles are algebraic structures used in the study of knots and 3-manifolds, particularly in the field of knot theory and topological quantum field theories. They provide a framework for understanding symmetries of knots and links through combinatorial methods. ### Birack A **birack** is a set \( X \) equipped with two binary operations \( \blacktriangledown \) and \( \blacktriangleleft \) that satisfy certain axioms.