Quantum knot mosaics and the growth constant
- Authors
- Oh, Seungsang
- Issue Date
- 1-9월-2016
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Quantum knot; Knot mosaic; Growth rate
- Citation
- TOPOLOGY AND ITS APPLICATIONS, v.210, pp.311 - 316
- Indexed
- SCIE
SCOPUS
- Journal Title
- TOPOLOGY AND ITS APPLICATIONS
- Volume
- 210
- Start Page
- 311
- End Page
- 316
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/87546
- DOI
- 10.1016/j.topol.2016.08.011
- ISSN
- 0166-8641
- Abstract
- Lomonaco and Kauffman introduced a knot mosaic system to give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This paper is inspired by an open question about the knot mosaic enumeration suggested by them. A knot n-mosaic is an nxn array of 11 mosaic tiles representing a knot or a link diagram by adjoining properly that is called suitably connected. The total number of knot n-mosaics is denoted by D-n which is known to grow in a quadratic exponential rate. In this paper, we show the existence of the knot mosaic constant delta = lim(n ->infinity) Dn1/n(2) and prove that 4 <= delta <= 5+root 13/2 (approximate to 4.303) (C) 2016 Elsevier B.V. All rights reserved.
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