Add to ORKGAbstract. Generalizing twist moves of classical knots, we introduce t(a1; ; am)-moves of virtual knots for an m{tuple (a1; ; am) of nonzero integers. In [4], M. Goussarov, M. Polyak and O. Viro introduced nite type invariants of virtual knots and Gauss diagram formulae giving combinatorial presentations of nite type invariants. By using the Gauss diagram formulae for the nite type invariants of degree 2, we give a necessary condition for a virtual long knot K to be transformed to a virtual long knot K 0 by a nite sequence of t(a1; ; am)-moves for an m-tuple (a1; ; am) of nonzero integers with the same sign. 1
AbstractWe introduce a polynomial invariant of long virtual knots that is non-trivial for many virtu...
Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interes...
A knot is an embedding of a circle into a 3-dimensional manifold. When this man- ifold is the sphere...
. We observe that any knot invariant extends to virtual knots. The isotopy classication problem for ...
The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have...
The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have...
AbstractWe observe that any knot invariant extends to virtual knots. The isotopy classification prob...
AbstractHomotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual k...
AbstractThis paper is an introduction to the theory of virtual knots. It is dedicated to the memory ...
In this paper, we examine Fox colorings of virtual knots, and moves called k-swap moves defined for ...
Abstract. We define new notions of groups of virtual and welded knots (or links) and we study their ...
Knot theory is an important branch of mathematics with applications in other branches of science. In...
In this paper, on the basis of the notion of parity introduced recently by the author, for each posi...
We construct various functorial maps (projections) from virtual knots to classical knots. These maps...
In this paper, on the basis of the notion of parity introduced recently by the author, for each posi...
AbstractWe introduce a polynomial invariant of long virtual knots that is non-trivial for many virtu...
Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interes...
A knot is an embedding of a circle into a 3-dimensional manifold. When this man- ifold is the sphere...
. We observe that any knot invariant extends to virtual knots. The isotopy classication problem for ...
The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have...
The present paper produces examples of Gauss diagram formulae for virtual knot invariants which have...
AbstractWe observe that any knot invariant extends to virtual knots. The isotopy classification prob...
AbstractHomotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual k...
AbstractThis paper is an introduction to the theory of virtual knots. It is dedicated to the memory ...
In this paper, we examine Fox colorings of virtual knots, and moves called k-swap moves defined for ...
Abstract. We define new notions of groups of virtual and welded knots (or links) and we study their ...
Knot theory is an important branch of mathematics with applications in other branches of science. In...
In this paper, on the basis of the notion of parity introduced recently by the author, for each posi...
We construct various functorial maps (projections) from virtual knots to classical knots. These maps...
In this paper, on the basis of the notion of parity introduced recently by the author, for each posi...
AbstractWe introduce a polynomial invariant of long virtual knots that is non-trivial for many virtu...
Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interes...
A knot is an embedding of a circle into a 3-dimensional manifold. When this man- ifold is the sphere...