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 × n matrix of 11 kinds of specific mosaic tiles representing a knot or a link by adjoining properly that is called suitably connected. Dn denotes the total number of all knot n-mosaics. Already known is that D1 = 1, D2 = 2 and D3 = 22. In this paper we establish the lower and upper bounds on Dn 2/275 (9 · 6n-2 + 1)2 · 2(n-3)2 ≤ Dn ≤ 2/275 (9 · 6n-2 + 1)2 · (4.4)(n-3)2 . and find the exact number of D4 = 2594.
|Journal||Journal of Knot Theory and its Ramifications|
|Publication status||Published - 2014 Nov 22|
- Quantum knot
- knot mosaic
- upper bound
ASJC Scopus subject areas
- Algebra and Number Theory