RECURSION FORMULAS FOR SOME ABELIAN KNOT INVARIANTS
2000 ◽
Vol 09
(03)
◽
pp. 413-422
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Keyword(s):
Let K be a tame knot in S3. We show that the sequence of cyclic resultants of the Alexander polynomial of K satisfies a linear recursion formula with integral coefficients. This means that the orders of the first homology groups of the branched cyclic covers of K can be computed recursively. We further establish the existence of a recursion formula that generates sequences which contain the square roots of the orders for the odd-fold covers that contain the square roots of the orders for the even-fold covers quotiented by the order for the two-fold cover. (That these square roots are all integers follows from a theorem of Plans.)
1993 ◽
Vol 87
(3)
◽
pp. 237-240
2008 ◽
Vol 17
(10)
◽
pp. 1199-1221
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2003 ◽
Vol 12
(06)
◽
pp. 805-817
1997 ◽
Vol 122
(2)
◽
pp. 281-290
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2009 ◽
Vol 18
(07)
◽
pp. 973-984
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2004 ◽
Vol 148
(1)
◽
pp. 163-171
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1986 ◽
Vol 40
◽
pp. 15-26
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2009 ◽
Vol 361
(09)
◽
pp. 4653-4681
1984 ◽
Vol 90
(3)
◽
pp. 440-440
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