Quantum knot mosaics and the growth constant

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5 Citations (Scopus)

Abstract

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→∞⁡Dn 1n2 and prove that4≤δ≤5+132(≈4.303).

Original languageEnglish
Pages (from-to)311-316
Number of pages6
JournalTopology and its Applications
Volume210
DOIs
Publication statusPublished - 2016 Sep 1

Keywords

  • Growth rate
  • Knot mosaic
  • Quantum knot

ASJC Scopus subject areas

  • Geometry and Topology

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