A state enumeration of the foil knot

Preprint English OPEN
Ramaharo, Franck; Rakotondrajao, Fanja;
  • Subject: Mathematics - Combinatorics | 57M25, 52C30

We split the crossings of the foil knot and enumerate the resulting states with a generating polynomial. Unexpectedly, the number of such states which consist of two components are given by the lazy caterer's sequence. This sequence describes the maximum number of plana... View more
  • References (15)
    15 references, page 1 of 2

    [1] C. Adams, The Knot Book, W. H. Freeman and Company, 1994.

    [2] S. Barr, Experiments in Topology, Thomas Y. Crowell Company, 1964.

    [3] A. Crans, B. Mellor and S. Ganzell, The forbidden number of a knot, Kyungpook Mathematical Journal 55 (2015), 485{506.

    [4] D. Denton and P. Doyle, Shadow movies not arising from knots, arXiv preprint, 2011, https://arxiv.org/abs/1106.3545.

    [5] P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett and A. Oceanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 239{ 246.

    [6] K. Gongopadhyay and R. Mishra, Knot Theory and Its Applications, American Mathematical Society, 2016.

    [7] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, 1994.

    [8] J. L. Jacobsen and P. Zinn-Justin, Matrix models and the enumeration of alternating tangles, Markov Processes and Related Fields 9 (2003), 301{310.

    [9] L. Kau man, Knots and Physics, World Scienti c Publishers, 1991.

    [10] L. Kau man, New invariants in the theory of knots, Amer. Math. Monthly 95 (1988), 195{242.

  • Metrics
    No metrics available
Share - Bookmark