Links with small lattice stick numbers

Kyungpyo Hong, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them. In this paper we consider every link in the cubic lattice. The lattice stick number sL(L) of a link L is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice. Huh and Oh found all knots whose lattice stick numbers are at most 14. They proved that only the trefoil knot 31and the figure-eight knot 41have lattice stick numbers of 12 and 14, respectively. In this paper we find all links with more than one component whose lattice stick numbers are at most 14. Indeed we prove combinatorically that sL(212) = 8, sL(212#212) = sL(623) = sL(633) = 12, sL(412) = 13, sL(512) = 14 and any other non-split links have stick numbers of at least 15.

Original languageEnglish
Article number155202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number15
DOIs
Publication statusPublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 IOP Publishing Ltd.

Keywords

  • cubic lattice
  • knot
  • stick number

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation

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