Upper bound on the total number of knot n-mosaics

Kyungpyo Hong, Seungsang Oh, Ho Lee, Hwa Jeong Lee

Research output: Contribution to journalArticlepeer-review

7 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. 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.

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

Bibliographical note

Funding Information:
The second author’s research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP) (No. 2011-0021795).

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0027989).

Publisher Copyright:
© 2014 World Scientific Publishing Company.

Keywords

  • Quantum knot
  • knot mosaic
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

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