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Period and toroidal knot mosaics

Title
Period and toroidal knot mosaics
Authors
Oh, SeungsangHong, KyungpyoLee, HoLee, Hwa JeongYeon, Mi Jeong
DGIST Authors
Lee, Hwa Jeong
Issue Date
2017-04
Citation
Journal of Knot Theory and its Ramifications, 26(5)
Type
Article
Article Type
Article
Keywords
Knot MosaicPolynomialsQuantum KnotQuantum KnotsToroidal Mosaic
ISSN
0218-2165
Abstract
Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on 'Quantum knots and mosaics' to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an m × n matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper, we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot (m,n)-mosaics for any positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We also analyze the asymptotics of the growth rates of their cardinality. © 2017 World Scientific Publishing Company.
URI
http://hdl.handle.net/20.500.11750/4206
DOI
10.1142/S0218216517500316
Publisher
World Scientific Publishing Co. Pte Ltd
Files:
There are no files associated with this item.
Collection:
School of Undergraduate Studies1. Journal Articles


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