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

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. 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

Keywords

  • Quantum knot
  • knot mosaic
  • upper bound

ASJC Scopus subject areas

  • Algebra and Number Theory

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