Period and toroidal knot mosaics
- Authors
- Oh, Seungsang; Hong, Kyungpyo; Lee, Ho; Lee, Hwa Jeong; Yeon, Mi Jeong
- Issue Date
- 4월-2017
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Quantum knot; knot mosaic; toroidal mosaic
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.26, no.5
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 26
- Number
- 5
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/84046
- DOI
- 10.1142/S0218216517500316
- 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 x 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.
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