Stick numbers of Montesinos knots
- Authors
- Lee, Hwa Jeong; No, Sungjong; Oh, Seungsang
- Issue Date
- 3월-2021
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Knot; stick number; rational tangle; Montesinos knot
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.30, no.03
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 30
- Number
- 03
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/128466
- DOI
- 10.1142/S0218216521500139
- ISSN
- 0218-2165
- Abstract
- Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of the minimal crossing number c(K): s(K) <= 2c(K). Huh and Oh found an improved upper bound: s(K) <= 3/2(c(K) + 1). Huh, No and Oh proved that s(K) <= c(K) + 2 for a 2-bridge knot or link K with at least six crossings. As a sequel to this study, we present an upper bound on the stick number of Montesinos knots and links. Let K be a knot or link which admits a reduced Montesinos diagram with c(K) crossings. If each rational tangle in the diagram has five or more index of the related Conway notation, then s(K) <= c(K) + 3. Furthermore, if K is alternating, then we can additionally reduce the upper bound by 2.
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