Upper bound on lattice stick number of knots
- Authors
- Hong, Kyungpyo; No, Sungjong; Oh, Seungsang
- Issue Date
- 7월-2013
- Publisher
- CAMBRIDGE UNIV PRESS
- Citation
- MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v.155, no.1, pp.173 - 179
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
- Volume
- 155
- Number
- 1
- Start Page
- 173
- End Page
- 179
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/102779
- DOI
- 10.1017/S0305004113000212
- ISSN
- 0305-0041
- Abstract
- The lattice stick number s(L)(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 s(L)(K) <= 3c(K) + 2. Moreover if K is a non-alternating prime knot, then s(L)(K) <= 3c(K) - 4.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.