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We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of " weight systems " , finding everything to be in agreement with the conjecture that " every weight system integrates ". 1. " Standard " Virtual Knots For " classical " finite type invariants of ordinary knots,… (More)

- FIONNTAN ROUKEMA
- 2008

Goussarov, Polyak, and Viro proved that finite type invariants of knots are " finitely multi-local " , meaning that on a knot diagram, sums of quantities, defined by local information, determine the value of the knot invariant ([2]). The result implies the existence of Gauss diagram combinatorial formulas for finite type invariants. This article presents a… (More)

- F. ROUKEMA
- 2009

Real finite type invariants have diagrammatic descriptions and relate to Lie Algebras. Analogues of the corresponding results for virtual finite type invariants exist, but are less well understood. This article collects computational results about the dimensions of the Polyak algebra and other spaces related to virtual finite type invariants. The code… (More)

- F. ROUKEMA
- 2009

The study of finite type invariants is central to the development of knot theory. Much of the theory still needs to be extended to the newer virtual context. In this article we calculate the dimensions of the spaces of virtual finite type knot invariants and associated graded algebras for several classes of virtual knots to orders four and five. The data… (More)

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