A Cn-MOVE FOR A KNOT AND THE COEFFICIENTS OF THE CONWAY POLYNOMIAL
2008 ◽
Vol 17
(07)
◽
pp. 771-785
◽
It is shown that two knots can be transformed into each other by Cn-moves if and only if they have the same Vassiliev invariants of order less than n. Consequently, a Cn-move cannot change the Vassiliev invariants of order less than n and may change those of order more than or equal to n. In this paper, we consider the coefficient of the Conway polynomial as a Vassiliev invariant and show that a Cn-move changes the nth coefficient of the Conway polynomial by ±2, or 0. And for the 2mth coefficient (2m > n), it can change by p or p + 1 for any given integer p.
2003 ◽
Vol 12
(06)
◽
pp. 767-779
◽
Keyword(s):
2006 ◽
Vol 15
(09)
◽
pp. 1215-1224
◽
2004 ◽
Vol 13
(06)
◽
pp. 719-735
Keyword(s):
2013 ◽
Vol 22
(05)
◽
pp. 1350017
◽
Keyword(s):
1994 ◽
Vol 03
(03)
◽
pp. 391-405
◽
1996 ◽
Vol 05
(04)
◽
pp. 421-425
◽
Keyword(s):
1999 ◽
Vol 08
(02)
◽
pp. 253-259
Keyword(s):
1999 ◽
Vol 08
(04)
◽
pp. 447-462
◽
2016 ◽
Vol 25
(08)
◽
pp. 1650045
Keyword(s):
1997 ◽
Vol 06
(05)
◽
pp. 687-714
◽