TY - JOUR
T1 - Quantum knot mosaics and the growth constant
AU - Oh, Seungsang
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( MSIP ) (No. NRF-2014R1A2A1A11050999 ).
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - 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 n×n 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 Dn which is known to grow in a quadratic exponential rate. In this paper, we show the existence of the knot mosaic constant δ=limn→∞Dn1n2 and prove that4≤δ≤5+132(≈4.303).
AB - 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 n×n 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 Dn which is known to grow in a quadratic exponential rate. In this paper, we show the existence of the knot mosaic constant δ=limn→∞Dn1n2 and prove that4≤δ≤5+132(≈4.303).
KW - Growth rate
KW - Knot mosaic
KW - Quantum knot
UR - http://www.scopus.com/inward/record.url?scp=84981485865&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2016.08.011
DO - 10.1016/j.topol.2016.08.011
M3 - Article
AN - SCOPUS:84981485865
SN - 0166-8641
VL - 210
SP - 311
EP - 316
JO - Topology and its Applications
JF - Topology and its Applications
ER -