Stick numbers of Montesinos knots

Hwa Jeong Lee, Sungjong No, Seungsang Oh

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number2150013
JournalJournal of Knot Theory and its Ramifications
Volume30
Issue number3
DOIs
Publication statusPublished - 2021 Mar

Bibliographical note

Funding Information:
Hwa Jeong Lee was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (No. 2019R1A2C1005506) and the Dongguk University Research Fund of 2019. Sungjong No was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government Ministry of Science and ICT (NRF-2020R1G1A1A01101724). Seungsang Oh was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. NRF-2017R1A2B2007216).

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

  • Knot
  • Montesinos knot
  • rational tangle
  • stick number

ASJC Scopus subject areas

  • Algebra and Number Theory

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