Linearized chord diagrams and an upper bound for Vassiliev invariants
Recently, Stoimenow [J. Knot Th. Ram. 7 (1998), 93-114] gave an upper bound on the dimension dn of the space of order n Vassiliev knot invariants, by considering chord diagrams of a certain type. We present a simpler argument which gives a better bound on the number of these chord diagrams, and hence on dn.
Journal of Knot Theory and its Ramifications
Bollobás, B., & Riordan, O. (2000). Linearized chord diagrams and an upper bound for Vassiliev invariants. Journal of Knot Theory and its Ramifications, 9 (7), 847-853. https://doi.org/10.1142/S0218216500000475