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 11(4) 507-514 2002年
By the same way for knots, it can be proved that if a link L is transformed into L′ by a Cn-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 Cn-m...
Journal of Knot Theory and its Ramifications 11(4) 515-526 2002年
In this paper, we show that when any nonnegative integer n and any knot K are given, there exist infinitely many unknotting number one knots Jm (m = 1, 2, ⋯) such that their Vassiliev invariants of order less than or equal to n coincide with those...