A318050 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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.

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.

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

KEYWORD

nonn,hard,more,tabf

AUTHOR

STATUS

approved