Add to ORKGIn this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied to it to reduce the number of crossings. We show that for an arbitrary diagram D of a link without a trivial split component, a minimal diagram obtained by applying Reidemeister moves I and II to D is unique. The proof also shows that the number of crossings of such a minimal diagram is unique for any diagram of any link. As the unknot admits infinitely many non-trivial minimal diagrams, we see that every link has infinitely many minimal diagrams, by considering the connected sums with such diagrams. We show that for a link without a trivial split component, an arbitrary Reidemeister move III either does not change the associated minimal diagr...
AbstractWe introduce a distance for diagrams of an oriented knot by using Reidemeister moves linking...
We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal ...
none2We extend the concept of diagrams and associated Reidemeister moves for links in the three-sphe...
In this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied t...
AbstractUsing unknotting number, we introduce a link diagram invariant of type given in Hass and Now...
We prove that there exist infinitely many pairs of RI-III related (see Definition 2.1 in this paper)...
Polyak proved that all oriented versions of Reidemeister moves for knot and link diagrams can be gen...
This paper has an experimental nature and contains no new theorems. We introduce certain moves for c...
We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister m...
In this paper we de. ne a partial ordering of knots and links using a special property derived from ...
none2We introduce the concept of regular diagrams for knots and links in lens spaces, proving that t...
In this paper we introduce a representation of knots and links called a cube diagram. We show that a...
We provide an upper bound on the number of ordered Reidemeister moves required to pass betw...
We consider diagrams of links in S² obtained by projection from S³ with the Hopf map and the minimal...
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equi...
AbstractWe introduce a distance for diagrams of an oriented knot by using Reidemeister moves linking...
We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal ...
none2We extend the concept of diagrams and associated Reidemeister moves for links in the three-sphe...
In this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied t...
AbstractUsing unknotting number, we introduce a link diagram invariant of type given in Hass and Now...
We prove that there exist infinitely many pairs of RI-III related (see Definition 2.1 in this paper)...
Polyak proved that all oriented versions of Reidemeister moves for knot and link diagrams can be gen...
This paper has an experimental nature and contains no new theorems. We introduce certain moves for c...
We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister m...
In this paper we de. ne a partial ordering of knots and links using a special property derived from ...
none2We introduce the concept of regular diagrams for knots and links in lens spaces, proving that t...
In this paper we introduce a representation of knots and links called a cube diagram. We show that a...
We provide an upper bound on the number of ordered Reidemeister moves required to pass betw...
We consider diagrams of links in S² obtained by projection from S³ with the Hopf map and the minimal...
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equi...
AbstractWe introduce a distance for diagrams of an oriented knot by using Reidemeister moves linking...
We construct a new order 1 invariant for knot diagrams. We use it to determine the minimal ...
none2We extend the concept of diagrams and associated Reidemeister moves for links in the three-sphe...