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Dimension of primitive Vassiliev knot invariants of order n.
(Formerly M0688)
4

%I M0688 #35 May 05 2022 04:47:13

%S 1,1,1,1,2,3,5,8,12,18,27,39,55

%N Dimension of primitive Vassiliev knot invariants of order n.

%C Next term is at least 78. - Jan Kneissler jk(AT)math.uni-bonn.de, Sep 1997

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H D. Bar-Natan, <a href="http://dx.doi.org/10.1016/0040-9383(95)93237-2">On the Vassiliev Knot Invariants</a>, Topology 34 (1995) 423-472.

%H D. Bar-Natan, <a href="http://www.pdmi.ras.ru/~duzhin/VasBib/">Bibliography of Vassiliev Invariants</a>.

%H Joan S. Birman, <a href="https://doi.org/10.1090/S0273-0979-1993-00389-6">New points of view in knot theory</a>, Bull. Amer. Math. Soc. (N.S.) 28 (1993), no. 2, 253-287; <a href="https://web.archive.org/web/20070527131321 /http://www.ams.org/journals/bull/pre-1996-data/199328-2/Birman">TeX source</a>.

%H D. J. Broadhurst, <a href="https://arxiv.org/abs/q-alg/9709031">Conjectured enumeration of Vassiliev invariants</a>, arXiv:q-alg/9709031, 1997.

%H S. Chmutov and S. Duzhin, <a href="http://dx.doi.org/10.1016/S0166-8641(97)00249-6">A lower bound for the number of Vassiliev knot invariants</a>, Topology and its Applications, Volume 92, Number 3, 14 April 1999, pp. 201-223(23).

%H Jan Kneissler, <a href="https://arxiv.org/abs/q-alg/9706022">The number of primitive Vassiliev invariants of degree up to 12</a>, arXiv:q-alg/9706022, 1997.

%H T. Ohtsuki (ed.), <a href="http://arxiv.org/abs/math/0406190">Problems on invariants of knots and 3-manifolds</a>, arXiv:math/0406190 [math.GT], (2004); see Table 2 on p.407.

%H <a href="/index/K#knots">Index entries for sequences related to knots</a>

%F Broadhurst gives a conjectured g.f.

%Y Cf. A014605, A050504.

%K hard,more,nonn,nice

%O 0,5

%A _N. J. A. Sloane_