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The writhe polynomial is a fundamental invariant of an oriented virtual knot.We introduce a kind of local moves for oriented virtual knots called shellmoves. The first aim of this paper is to prove that two oriented virtual knotshave the same writhe polynomial if and only if they are related by a finitesequence of shell moves. The second aim of this paper is to classify oriented$2$-component virtual links up to shell moves by using several invariants ofvirtual links.

Writhe polynomials and shell moves for virtual knots and links