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Dimension of space of weight systems of chord diagrams.
(Formerly M2356)
5

%I M2356 #35 Dec 26 2021 21:38:39

%S 1,0,1,1,3,4,9,14,27,44,80,132,232

%N Dimension of space of weight systems of chord diagrams.

%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 J. S. Birman, <a href="/A007293/a007293.pdf">Letter to N. J. A. Sloane, Apr 09 1994</a>

%H J. S. Birman, <a href="https://www.ams.org/journals/bull/1993-28-02/S0273-0979-1993-00389-6/home.html">New points of view in knot theory.</a>. Bulletin of the American Mathematical Society 28.2 (1993): 253-287.

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

%H Jan Kneissler, <a href="http://arxiv.org/abs/q-alg/9706022v1">The number of primitive Vassiliev invariants of degree up to 12</a>

%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 3 on p.408.

%H Evert Stenlund, <a href="http://www.evertstenlund.se/knots/On%20the%20Vassiliev%20Invariant.pdf">On the Vassiliev Invariants</a>, June 2017.

%H S. D. Tyurina, <a href="https://doi.org/10.1007/s10958-006-0095-9">Diagram invariants of knots and the Kontsevich integral</a>, J. Math. Sci. 134 (2) (2006) 2017-2017, Table 1.

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

%F Broadhurst gives a conjectured g.f.

%Y Cf. A007473, A007478.

%Y Cf. A014596.

%K nonn,more

%O 0,5

%A _N. J. A. Sloane_

%E Description corrected by _Sergei Duzhin_, Aug 29 2000