Upper bound on the total number of knot n-mosaics

Kyungpyo Hong, Seung Sang Oh, Ho Lee, Hwa Jeong Lee

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 × n matrix of 11 kinds of specific mosaic tiles representing a knot or a link by adjoining properly that is called suitably connected. D<inf>n</inf> denotes the total number of all knot n-mosaics. Already known is that D<inf>1</inf> = 1, D<inf>2</inf> = 2 and D<inf>3</inf> = 22. In this paper we establish the lower and upper bounds on D<inf>n</inf> 2/275 (9 · 6<sup>n-2</sup> + 1)<sup>2</sup> · 2<sup>(n-3)2</sup> ≤ Dn ≤ 2/275 (9 · 6<sup>n-2</sup> + 1)<sup>2</sup> · (4.4)<sup>(n-3)2</sup> . and find the exact number of D<inf>4</inf> = 2594.

Original languageEnglish
Article number1450065
JournalJournal of Knot Theory and its Ramifications
Volume23
Issue number13
DOIs
Publication statusPublished - 2014 Nov 22

Fingerprint

Knot
Upper bound
Tile
Quantum Systems
Upper and Lower Bounds
Denote

Keywords

  • knot mosaic
  • Quantum knot
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Upper bound on the total number of knot n-mosaics. / Hong, Kyungpyo; Oh, Seung Sang; Lee, Ho; Lee, Hwa Jeong.

In: Journal of Knot Theory and its Ramifications, Vol. 23, No. 13, 1450065, 22.11.2014.

Research output: Contribution to journalArticle

Hong, Kyungpyo ; Oh, Seung Sang ; Lee, Ho ; Lee, Hwa Jeong. / Upper bound on the total number of knot n-mosaics. In: Journal of Knot Theory and its Ramifications. 2014 ; Vol. 23, No. 13.
@article{dd16769a14b440d099aa33123c6a1ce9,
title = "Upper bound on the total number of knot n-mosaics",
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 × 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.",
keywords = "knot mosaic, Quantum knot, upper bound",
author = "Kyungpyo Hong and Oh, {Seung Sang} and Ho Lee and Lee, {Hwa Jeong}",
year = "2014",
month = "11",
day = "22",
doi = "10.1142/S0218216514500655",
language = "English",
volume = "23",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "13",

}

TY - JOUR

T1 - Upper bound on the total number of knot n-mosaics

AU - Hong, Kyungpyo

AU - Oh, Seung Sang

AU - Lee, Ho

AU - Lee, Hwa Jeong

PY - 2014/11/22

Y1 - 2014/11/22

N2 - 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.

AB - 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.

KW - knot mosaic

KW - Quantum knot

KW - upper bound

UR - http://www.scopus.com/inward/record.url?scp=84929579184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929579184&partnerID=8YFLogxK

U2 - 10.1142/S0218216514500655

DO - 10.1142/S0218216514500655

M3 - Article

VL - 23

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 13

M1 - 1450065

ER -