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math.GT2010
Parity and Exotic Combinatorial Formulae for Finite-Type Invariants of Virtual Knots
Micah Chrisman, Vassily Olegovich Manturov
The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have no analogue in the classical knot case. These combinatorial formulae contain ad…
math.GT2010
On the Goussarov-Polyak-Viro Finite-Type Invariants and the Virtualization Move
Micah W. Chrisman
In this paper, it is shown that there are no nonconstant Goussarov-Polyak-Viro finite-type invariants that are invariant under the virtualization move. As an immediate corollary, w…