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A007473 Dimension of space of Vassiliev knot invariants of order n.
(Formerly M0765)
2

%I M0765 #28 Jul 05 2023 17:05:26

%S 1,1,2,3,6,10,19,33,60,104,184,316,548

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

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

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

%H Dror Bar-Natan, <a href="http://www.math.toronto.edu/~drorbn/VasBib/VasBib.html">Bibliography of Vassiliev Invariants</a>

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

%H Maksim Karev, <a href="https://arxiv.org/abs/2307.00468">On the primitive subspace of Lando framed graph bialgebra</a>, arXiv:2307.00468 [math.CO], 2023.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/VassilievInvariant.html">Vassiliev Invariant.</a>

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

%F G.f.: Product_{ m >= 1 } (1-y^m)^(-A007478(m)). - _Andrey Zabolotskiy_, Sep 19 2017

%F Broadhurst gives a conjectured explicit g.f. (different from A014595).

%Y Cf. A007293 (first differences), A007478, A014595 (conjectured continuation).

%K hard,nonn,nice

%O 0,3

%A _N. J. A. Sloane_

%E Description corrected by _Sergei Duzhin_, Aug 29 2000

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Last modified April 23 07:42 EDT 2024. Contains 371905 sequences. (Running on oeis4.)