Rotationally Symmetric Rose Links
نویسنده
چکیده
This paper is an introduction to rose links and some of their properties. We used a series of invariants to distinguish some rose links that are rotationally symmetric. We were able to distinguish all 3-component rose links and narrow the bounds on possible distinct 4 and 5-component rose links to between 2 and 8, and 2 and 16, respectively. An algorithm for drawing rose links and a table of rose links with up to five components are included. Acknowledgements: The initial cursory observations on rose links were made during the 2011 Dr. Albert H. and Greta A. Bryan Summer Research Program at Simpson College in conjunction with fellow students Michael Comer and Jes Toyne, with Dr. William Schellhorn serving as research advisor. The research presented in this paper, including developing the definitions and related concepts about rose links and applying invariants, was conducted as a part of the author’s senior research project at Simpson College, again under the advisement of Dr. Schellhorn. The author would like to thank Dr. Schellhorn for his help and support, especially for his assistance with the definitions involving polygonal diagrams. Page 28 RHIT Undergrad. Math. J., Vol. 14, No. 1 Figure 1: The unknot is the simplest knot.
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