|
|||||
 |
|
|
|
|
|
A new partial
ordering of knots
Arazelle Mendoza, Tara Sargent, John Travis Shrontz and Paul Drube
Vol. 8 (2015), No. 3, 447–466
|
Abstract |
|
Our research concerns how knots behave under crossing changes. In particular, we investigate a partial ordering of alternating knots that results from performing crossing changes. A similar ordering was originally introduced by Kouki Taniyama in the paper “A partial order of knots”. We amend Taniyama’s partial ordering and present theorems about the structure of our ordering for more complicated knots. Our approach is largely graph theoretic, as we translate each knot diagram into one of two planar graphs by checkerboard coloring the plane. Of particular interest are the class of knots known as pretzel knots, as well as knots that have only one direct minor in the partial ordering. |
Keywords
knots, links, crossing changes
|
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
|
Milestones
Received: 21 June 2013
Revised: 30 March 2014
Accepted: 2 April 2014
Published: 5 June 2015
Communicated by Józef H. Przytycki
|
Authors |
| Arazelle Mendoza | |
| Christopher Newport University Newport News, VA 23606 United States |
|
| Tara Sargent | |
| Clarke University Dubuque, IA 52001 United States |
|
| John Travis Shrontz | |
| University of Alabama in
Huntsville Huntsville, AL 35816 United States |
|
| Paul Drube | |
| Department of Mathematics and
Computer Science Valparaiso University 1900 Chapel Drive Valparaiso, IN 46383 United States |
|
|
