An enumeration process for racks. Given a presentation for a rack (mathcal R), we define a process which systematically enumerates the elements of (mathcal R). The process is modeled on the systematic enumeration of cosets first given by Todd and Coxeter. This generalizes and improves the diagramming method for (n)-quandles introduced by Winker. We provide pseudocode that is similar to that given by Holt, Eick, and O’Brien for the Todd-Coxeter process. We prove that the process terminates if and only if (mathcal R) is finite, in which case, the procedure outputs an operation table for the finite rack. We conclude with an application to knot theory.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element