Knots with small lattice stick numbers

Youngsik Huh, Seung Sang Oh

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot 31 and in figure 8 knot 41 are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.

Original languageEnglish
Article number265002
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number26
DOIs
Publication statusPublished - 2010 Jun 16

Fingerprint

Knot
polygons
cubic lattices
Trefoil
Line segment
Straight Line
Polygon
Figure
Verify

ASJC Scopus subject areas

  • Mathematical Physics
  • Modelling and Simulation
  • Statistics and Probability
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Knots with small lattice stick numbers. / Huh, Youngsik; Oh, Seung Sang.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 26, 265002, 16.06.2010.

Research output: Contribution to journalArticle

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