Upper bound on lattice stick number of knots

Kyungpyo Hong, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The lattice stick number sL(K) of a knot K is defined to be the minimal number of straight line segments required to construct a stick presentation of K in the cubic lattice. In this paper, we find an upper bound on the lattice stick number of a nontrivial knot K, except the trefoil knot, in terms of the minimal crossing number c(K) which is sL(K) ≤ 3c(K) + 2. Moreover if K is a non-alternating prime knot, then sL(K) ≤ 3c(K) - 4.

Original languageEnglish
Pages (from-to)173-179
Number of pages7
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume155
Issue number1
DOIs
Publication statusPublished - 2013 Jul

ASJC Scopus subject areas

  • Mathematics(all)

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