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A KNOT INVARIANT DERIVED FROM GAMMA MOVES

T. Tanaka

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Abstract

Any knot can be changed into either the unknot or the trefoil knot by a finite sequence of gamma moves.We define the gamma index of a knot as the minimum number of moves among all such sequences.We show that the gamma indices of the knots 4 1 , 5 2 , 6 1 and 6 3 are equal to one and the gamma index of the connected sum of the trefoil knot and its mirror image is equal to two.

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Any knot can be changed into either the unknot or the trefoil knot by a finite sequence of gamma moves.We define the gamma index of a knot as the minimum number of moves among all such sequences.We show that the gamma indices of the knots 4 1 , 5 2 , 6 1 and 6 3 are equal to one and the gamma index of the connected sum of the trefoil knot and its mirror image is equal to two.

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Available abstract

Any knot can be changed into either the unknot or the trefoil knot by a finite sequence of gamma moves.We define the gamma index of a knot as the minimum number of moves among all such sequences.We show that the gamma indices of the knots 4 1 , 5 2 , 6 1 and 6 3 are equal to one and the gamma index of the connected sum of the trefoil knot and its mirror image is equal to two.

Key concepts: Unknot, Trefoil knot, Knot (papermaking), Tricolorability, Mathematics, Trefoil, Knot invariant, Combinatorics

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