The Second Reidemeister Moves and Colorings of Virtual Knot Diagrams
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Two virtual knot diagrams are said to be equivalent, if there is a sequence S of Reidemeister moves and virtual moves relating them. The difference of writhes of the two virtual knot diagrams gives a lower bound for the number of the first Reidemeister moves in S. In previous work, we introduced a polynomial qK(t) for a virtual knot diagram K which gave a lower bound for the number of the third Reidemeister moves in the sequence S. In this paper we define a new polynomial from a coloring of a virtual knot diagram. Using this polynomial, we give a lower bound for the number of the second Reidemeister moves in S. The polynomial also suggests the design of the sequence S.
Abstract
Two virtual knot diagrams are said to be equivalent, if there is a sequence S of Reidemeister moves and virtual moves relating them. The difference of writhes of the two virtual knot diagrams gives a lower bound for the number of the first Reidemeister moves in S. In previous work, we introduced a polynomial qK(t) for a virtual knot diagram K which gave a lower bound for the number of the third Reidemeister moves in the sequence S. In this paper we define a new polynomial from a coloring of a virtual knot diagram. Using this polynomial, we give a lower bound for the number of the second Reidemeister moves in S. The polynomial also suggests the design of the sequence S.
참고문헌 (10)
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