Journal of Knot Theory and Its Ramifications 28(12) 1950074-1950074 2019年10月 [査読有り]
Satoh and Taniguchi introduced the [Formula: see text]-writhe [Formula: see text] for each non-zero integer [Formula: see text], which is an invariant for virtual knots. The [Formula: see text]-writhes give the coefficients of some polynomial inva...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 26(13) 2017年11月 [査読有り]
We consider a local move, denoted by., on knot diagrams or virtual knot diagrams. If two (virtual) knots K-1 and K-2 are transformed into each other by a finite sequence of lambda moves, the lambda distance between K-1 and K-2 is the minimum numbe...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 23(4) 2014年4月 [査読有り]
A local move called a C-n-move is closely related to Vassiliev invariants. The C-n-distance between two knots K and L, denoted by d(Cn) (K, L), is the minimal number of C-n-moves needed to transform K into L. In the case of n >= 3, we show that...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 15(1) 73-80 2006年1月
Hirasawa, and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S-3 by using "a crossing change". In this paper, we define the C-k-Gordian complex of knots which is an extension o...
Journal of Knot Theory and its Ramifications 15(1) 73-80 2006年1月
Hirasawa and Uchida defined the Gordian complex of knots which is a simplicial complex whose vertices consist of all knot types in S3 by using "a crossing change". In this paper, we define the C ke-Gordian complex of knots which is an extension of...
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 55(3) 641-654 2003年7月
In this note, we will study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition was given by a pair of numerical invariants derived from the Conway polynomials for two link ty...
Journal of the Mathematical Society of Japan 55(3) 641-654 2003年
In this note, we will study Delta link homotopy, which is an equivalence relation of ordered and oriented link types. Previously, a necessary condition was given by a pair of numerical invariants derived from the Conway polynomials for two link ty...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 11(4) 507-514 2002年6月
By the same way for knots, it can be proved that if a link L is transformed into L' by a C-n-move, the difference of the Vassiliev invariants of order n between L and L' is equal to the value of the one-branch tree diagram corresponding to the C-n...
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