Link lengths and their growth powers

Youngsik Huh, Sungjong No, Seungsang Oh, Eric J. Rawdon

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)

    Abstract

    For a certain infinite family F of knots or links, we study the growth power ratios of their stick number, lattice stick number, minimum lattice length and minimum ropelength compared with their minimum crossing number c(K) for every K ∈ F. It is known that the stick number and lattice stick number grow between the 1/2 and linear power of the crossing number, and minimum lattice length and minimum ropelength grow with at least the 3/4 power of crossing number (which is called the four-thirds power law). Furthermore, the minimal lattice length and minimum ropelength grow at most as O (c (K)[ln(c (K))]5), but it is unknown whether any family exhibits superlinear growth. For any real number r between 1/2 and 1, we give an infinite family of non-splittable prime links in which the stick number and lattice stick number grow exactly as the rth power of crossing number. Furthermore for any real number r between 3/4 and 1, we give another infinite family of non-splittable prime links in which the minimum lattice length and minimum ropelength grow exactly as the rth power of crossing number.

    Original languageEnglish
    Article number035202
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume48
    Issue number3
    DOIs
    Publication statusPublished - 2015 Jan 23

    Bibliographical note

    Publisher Copyright:
    © 2015 IOP Publishing Ltd.

    Keywords

    • minimum lattice length
    • ropelength
    • stick number

    ASJC Scopus subject areas

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

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