Enumeration on graph mosaics

Kyungpyo Hong, Seung Sang Oh

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is intended to represent an actual physical quantum system. Recently the authors developed an algorithm producing the exact enumeration of knot mosaics, which uses a recursion formula of state matrices. As a sequel to this research program, we similarly define the (embedded) graph mosaic system by using 16 graph mosaic tiles, representing graph diagrams with vertices of valence 3 and 4. We extend the algorithm to produce the exact number of all graph mosaics. The magnified state matrix that is an extension of the state matrix is mainly used.

Original languageEnglish
JournalJournal of Knot Theory and its Ramifications
DOIs
Publication statusAccepted/In press - 2017

Fingerprint

Enumeration
Knot
Graph in graph theory
Exact Enumeration
Jones Polynomial
Knot Theory
Embedded Graph
Recursion Formula
Quantum Physics
Tile
Quantum Systems
Diagram

Keywords

  • graph mosaic
  • knot mosaic
  • Quantum knot

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Enumeration on graph mosaics. / Hong, Kyungpyo; Oh, Seung Sang.

In: Journal of Knot Theory and its Ramifications, 2017.

Research output: Contribution to journalArticle

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