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I study a am studying virtual knot theory. A virtual knot is an immersion a knot diagram with real or virtual crossing information. The equivalence relation made by includes generalized Reidemeister moves. The There are premitted virtual Reidemeister movesdo not admit , and forbbiden moves.

Question

Do the forbidden moves have some varildityvalidity? How are generalized Reidemeister moves made? For example, If we admit the moves the virtual knot is trivial. Therefore, we make fobbiden some of the moves forbidden. The moves have two real virtual crossings and one virtual crossing. However, instead of the these moves, why the other moves are not selected? For instance, May may we remove exclude classical Reidemeister I move instead of forbbiden the forbidden moves? I confuseam confused!

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# Validity of generalized Reidemeister moves for a virtual knot

I study a virtual knot theory. A virtual knot is an immersion with real or virtual crossing information. The equivalence relation made by generalized Reidemeister moves. The moves do not admit forbbiden moves.

Question

Do the forbidden moves have some varildity? How are generalized Reidemeister moves made? For example, If we admit the moves the virtual knot is trivial. Therefore, we make fobbiden moves. The moves have two real virtual crossings and one virtual crossing. However, instead of the moves, why the other moves are not selected? For instance, May we remove classical Reidemeister I move instead of forbbiden moves? I confuse!