Upper bound on the total number of knot n-mosaics
- Authors
- Hong, Kyungpyo; Oh, Seungsang; Lee, Ho; Lee, Hwa Jeong
- Issue Date
- 11월-2014
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Quantum knot; knot mosaic; upper bound
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.23, no.13
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 23
- Number
- 13
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/96883
- DOI
- 10.1142/S0218216514500655
- ISSN
- 0218-2165
- Abstract
- Lomonaco and Kauffman introduced a knot mosaic system to give a definition of a quantum knot system which can be viewed as a blueprint for the construction of an actual physical quantum system. A knot n-mosaic is an n x n matrix of 11 kinds of specific mosaic tiles representing a knot or a link by adjoining properly that is called suitably connected. D-n denotes the total number of all knot n-mosaics. Already known is that D-1 = 1, D-2 = 2 and D-3 = 22. In this paper we establish the lower and upper bounds on D-n 2/275 (9.6(n-2) + 1)(2) . 2((n-3)2) <= D-n <= 2/275 (9 . 6(n-2) + 1)(2) . (4.4)((n-3)2). and find the exact number of D-4 = 2594.
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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