Period and toroidal knot mosaics

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

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on 'Quantum knots and mosaics' to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an m × n matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper, we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot (m,n)-mosaics for any positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We also analyze the asymptotics of the growth rates of their cardinality.

Original languageEnglish
Article number1750031
JournalJournal of Knot Theory and its Ramifications
Issue number5
Publication statusPublished - 2017 Apr 1

Bibliographical note

Funding Information:
The corresponding author(Seungsang Oh) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. NRF-2014R1A2A1A11050999). Hwa Jeong Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF- 2015R1C1A2A01054607).

Publisher Copyright:
© 2017 World Scientific Publishing Company.


  • Quantum knot
  • knot mosaic
  • toroidal mosaic

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Period and toroidal knot mosaics'. Together they form a unique fingerprint.

Cite this