A318050 Triangle read by rows: T(n,k) is the number of prime knots with n crossings whose unknotting numbers are k.

0, 1, 0, 1, 0, 1, 1, 0, 3, 0, 3, 3, 1, 0, 9, 11, 1, 0, 17, 22, 9, 1

Offset

3,9

Comments

The unknotting number of a knot is the minimal number of crossing switches required to convert a knot into the unknot (0 crossing).

Row n is a partition of A002863(n).

Row 10 cannot yet be completed because the unknotting number of some knots are still unknown.

References

P. R. Cromwell, Knots and Links, Cambridge University Press, 2004, pp. 151-154.

Links

Table of n, a(n) for n=3..24.

S. A. Bleiler, A note on unknotting number, Math. Proc. Camb. Phil. Soc. Vol. 96 (1984).

M. Borodzik and S. Friedl, The unknotting number and classical invariants, I, Algebraic and Geometric Topology Vol. 15 (2015), 85-135.

J. C. Cha and C. Livingston, KnotInfo: Table of Knot Invariants.

S. Jablan and L. Radovic, Unknotting numbers of alternating knot and link families, Publications de l'Institut Mathématiques, Nouvelle série, tome 95 (2014), 87-99.

K. Murasugi, On a certain numerical invariant of link types, Trans. Am. Math. Soc. Vol. 117 (1965), 387-422.

Eric Weisstein's World of Mathematics, Unknotting Number.

Index entries for sequences related to knots

Example

Triangle begins:
n\k|  0   1   2   3   4
---+-------------------
3  |  0   1
4  |  0   1
5  |  0   1   1
6  |  0   3
7  |  0   3   3   1
8  |  0   9  11   1
9  |  0  17  22   9   1

Crossrefs

Cf. A002863, A078477, A089797, A089891, A089892, A173466, A318051, A318052.

Sequence in context: A127801 A096597 A097994 * A053604 A066958 A357062

Adjacent sequences: A318047 A318048 A318049 * A318051 A318052 A318053

Keyword

nonn,hard,more,tabf

Author

Franck Maminirina Ramaharo, Aug 14 2018

Status

approved