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 17(7) 771-785 2008年7月
It is shown that two knots can be transformed into each other by C-n-moves if and only if they have the same Vassiliev invariants of order less than n. Consequently, a C-n-move cannot change the Vassiliev invariants of order less than n and may ch...
Journal of Knot Theory and its Ramifications 15(9) 1215-1224 2006年11月
By the works of Gusarov [2] and Habiro [3], it is known that a local move called the Cn move is strongly related to Vassiliev invariants of order less than n. The coefficient of the zn term in the Conway polynomial is known to be a Vassiliev invar...
Journal of Knot Theory and its Ramifications 15(9) 1215-1224 2006年11月
By the works of Gusarov [2] and Habiro [3], it is known that a local move called the Cn move is strongly related to Vassiliev invariants of order less than n. The coefficient of the zn term in the Conway polynomial is known to be a Vassiliev invar...
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 15(2) 205-215 2006年2月
It is well-known that the coefficient of z(m) of the Conway polynomial is a Vassiiev invariant of order m. In this paper, we show that for any given pair of a natural number n and a knot K, there exist infinitely many knots whose Vassiliev invaria...
Journal of Knot Theory and its Ramifications 15(2) 205-215 2006年2月
It is well-known that the coefficient of zm of the Conway polynomial is a Vassiiev invariant of order m. In this paper, we show that for any given pair of a natural number n and a knot K, there exist infinitely many knots whose Vassiliev invariant...