OFFSET
3,10
COMMENTS
The signature of a knot is a classical lower bound for the unknotting number of knots. If sigma(K) and u(K) denote the signature and the unknotting number of the knot K, respectively, then 0 <= (1/2)*abs(sigma(K)) <= u(K). If one can empirically find an unknotting number u*(K) = (1/2)*abs(sigma(K)), then it is its exact value.
Row n is a partition of A002863(n).
REFERENCES
P. R. Cromwell, Knots and Links, Cambridge University Press, 2004, pp. 151-154.
W. B. R. Lickorish, An introduction to Knot Theory, Springer, 1997, Table 8.1, p. 85.
LINKS
J. C. Cha and C. Livingston, KnotInfo: Table of Knot Invariants
J. C. Cha and C. Livingston, Signature
K. Murasugi, On a certain numerical invariant of link types, Trans. Am. Math. Soc. Vol. 117 (1965), 387-422.
A. Stoimenow, Table of the signature
Eric Weisstein's World of Mathematics, Knot Signature
Wikipedia, Signature of a knot
EXAMPLE
Triangle begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10
---+--------------------------------------------
3 | 0 0 1
4 | 1
5 | 0 0 1 0 1
6 | 2 0 1
7 | 1 0 3 0 2 0 1
8 | 9 0 8 0 3 0 1
9 | 11 0 21 0 12 0 4 0 1
10 | 54 0 68 0 32 0 10 0 1
11 | 148 0 228 0 124 0 44 0 7 0 1
12 | 619 0 900 0 461 0 162 0 34
CROSSREFS
KEYWORD
nonn,hard,more,tabf
AUTHOR
Franck Maminirina Ramaharo, Aug 14 2018
STATUS
approved