Document Type
Article - post-print
Publication Date
2019
Abstract
Given a presentation for a rack , we define a process which systematically enumerates the elements of . The process is modeled on the systematic enumeration of cosets first given by Todd and Coxeter. This generalizes and improves the diagramming method for -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 is finite, in which case, the procedure outputs an operation table for the finite rack. We conclude with an application to knot theory
Original Publication Citation
HOSTE, JIM, and PATRICK D. SHANAHAN. “An Enumeration Process for Racks.” Mathematics of Computation, vol. 88, no. 317, May 2019, pp. 1427–1448. doi:10.1090/mcom/3374.
Digital Commons @ LMU & LLS Citation
Shanahan, Patrick, "An enumeration process for racks" (2019). Mathematics, Statistics and Data Science Faculty Works. 164.
https://digitalcommons.lmu.edu/math_fac/164
