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MINIMAL SETS OF REIDEMEISTER MOVES
, 908
"... Abstract. It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves Ω1, Ω2 and Ω3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the Ω1 and Ω2 moves, and 8 vers ..."
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Abstract. It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves Ω1, Ω2 and Ω3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the Ω1 and Ω2 moves, and 8
AN UPPER BOUND ON REIDEMEISTER MOVES
"... Abstract. We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links. 1. ..."
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Cited by 2 (2 self)
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Abstract. We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links. 1.
A BOUND FOR ORDERINGS OF REIDEMEISTER MOVES
"... Abstract. We provide an upper bound on the number of ordered Reidemeister moves required to pass between two diagrams of the same link. This bound is in terms of the number of unordered Reidemeister moves required. In 1927 Kurt Reidemeister proved that any two link diagrams representing the same lin ..."
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Abstract. We provide an upper bound on the number of ordered Reidemeister moves required to pass between two diagrams of the same link. This bound is in terms of the number of unordered Reidemeister moves required. In 1927 Kurt Reidemeister proved that any two link diagrams representing the same
The number of Reidemeister Moves Needed for Unknotting
, 2008
"... There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c1n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K embe ..."
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Cited by 45 (11 self)
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There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c1n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K
HOMOLOGY INVARIANCE UNDER REIDEMEISTER MOVES
, 2005
"... Abstract. This paper is an undergraduate thesis, the goal of which is not to develop new research perse but to exhibit, through the completion of a proof, thorough understanding of topics somewhat more advanced than the accepted level of undergraduate study. My particular endeavor involved a close e ..."
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examination of the two papers, On Khovanov’s Categorification of the Jones Polynomial and Khovanov’s Homology for Tangles and Cobordisms, both authored by BarNatan. While the proof that homology (of the knot projection) is invariant under Reidemeister moves is outlined in the latter of these papers
Ordering the Reidemeister moves of a classical knot
 2006), 659–671 (electronic). MR 2240911 (2007d:57010
"... We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type. 57M25; 57M27 It is one of the founding theorems of knot theory that any two diagrams of a given link may be changed from one into the other by a sequence of Reidemeister ..."
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We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type. 57M25; 57M27 It is one of the founding theorems of knot theory that any two diagrams of a given link may be changed from one into the other by a sequence
Invariants Of Knot Diagrams And Relations Among Reidemeister Moves
 J. Knot Theory Ramifications
"... In this paper a classification of Reidemeister moves, which is the most refined, is introduced. In particular, this classification distinguishes some # 3 moves that only di#er in how the three strands that are involved in the move are ordered on the knot. ..."
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Cited by 23 (0 self)
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In this paper a classification of Reidemeister moves, which is the most refined, is introduced. In particular, this classification distinguishes some # 3 moves that only di#er in how the three strands that are involved in the move are ordered on the knot.
Unknotting number and number of Reidemeister moves . . .
 TOPOLOGY AND ITS APPLICATIONS
, 2012
"... ..."
A lower bound for the number of Reidemeister moves for unknotting
 J. Knot Theory Ramif
, 2006
"... I would like to thank him for his encouragement, and letting me study anything I like when I was a student. Abstract. How many Reidemeister moves do we need for unknotting a given diagram of the trivial knot? Hass and Lagarias gave an upper bound. We give an upper bound for deforming a diagram of a ..."
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I would like to thank him for his encouragement, and letting me study anything I like when I was a student. Abstract. How many Reidemeister moves do we need for unknotting a given diagram of the trivial knot? Hass and Lagarias gave an upper bound. We give an upper bound for deforming a diagram of a
Results 1  10
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