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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 102, Issue 2
  • September 1987, pp. 303-315

The growth of the number of prime knots

  • C. Ernst (a1) and D. W. Sumners (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100067323
  • Published online: 24 October 2008
Abstract

A fundamental and interesting question in knot theory is:

Question 1. How many prime knots of n crossings are there ?

Over time, knot theorists have answered this question for n ≤ 13 by the method of exhaustion: one writes down a list of all possible knots of n crossings, and then works hard to eliminate duplications from the list [12]. A perhaps easier question is the following:

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[6]J. P. J. Michels and F. W. Wiegel . Probability of knots in a polymer ring. Phys. Lett. A 90 (1982).

[8]H. Schubert . Knoten mit zwei brucken. Math. Z. 65 (1956), 133170.

[10]S. J. Spengler , A. Stasiak and N. R. Cozzarelli . The stereostructure of knots and catenanes produced by phage λ integrative recombination: implications for mechanism and DNA structure. Cell 42 (1985), 325334.

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