An enumeration process for racks
| Autor: | Jim Hoste, Patrick D. Shanahan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
Applied Mathematics 010102 general mathematics Coxeter group Process (computing) Geometric Topology (math.GT) 01 natural sciences Mathematics::Geometric Topology Knot theory Rack Combinatorics Computational Mathematics Mathematics - Geometric Topology If and only if 0103 physical sciences 57M25 Enumeration FOS: Mathematics Coset 010307 mathematical physics 0101 mathematics Pseudocode Mathematics |
| Popis: | 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 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. 23 pages, 3 figures, pseudocode included, article revised according to referees suggestions, section 5 on modifications expanded and new section 7 on python implementation and performance added. Ancillary file contains python code |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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