Small knot mosaics and partition matrices
- Authors
- Hong, Kyungpyo; Lee, Ho; Lee, Hwa Jeong; Oh, Seungsang
- Issue Date
- 31-10월-2014
- Publisher
- IOP PUBLISHING LTD
- Keywords
- quantum physics; quantum knot; knot mosaic; partition matrix
- Citation
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, v.47, no.43
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Volume
- 47
- Number
- 43
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/97042
- DOI
- 10.1088/1751-8113/47/43/435201
- ISSN
- 1751-8113
- Abstract
- Lomonaco and Kauffman introduced knot mosaic system to give a definition of quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m, n)-mosaic is an m x n matrix of mosaic tiles which are T-0 through T-10 depicted, representing a knot or a link by adjoining properly that is called suitably connected. An interesting question in studying mosaic theory is how many knot (m, n)-mosaics are there. D-m,D- (n) denotes the total number of all knot (m, n)-mosaics. This counting is very important because the total number of knot mosaics is indeed the dimension of the Hilbert space of these quantum knot mosaics. In this paper, we find a table of the precise values of D-m,D- n for 4 <= m <= n <= 6. Mainly we use a partition matrix argument which turns out to be remarkably efficient to count small knot mosaics.
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