A173637 Conway notation for rational 2-component links.

2, 4, 212, 6, 33, 222, 412, 3112, 232, 8, 53, 422, 323, 3122, 242, 21212, 211112, 612, 5112, 432, 414, 4113, 3312, 32112, 3132, 31113, 252, 22212, 221112

Offset: 1

Author

Jonathan Vos Post, Nov 23 2010

Keywords

• nonn

Comments

The ordering of the list is based on increasing crossing numbers and inverse lexicographical order for the terms with the same crossing number.

This is to links what A122495 is to knots.

All these links are chiral.

Each term is actually an ordered set of positive integers, concatenated; as long as all integers are 1-digit, it's not a problem, but a(30) requires "digit" 10, so at that point the sequence becomes not fully well-defined. An irregular array of these numbers would be well-defined.

Number of the terms of this sequence with crossing number k plus number of the terms of A122495 with crossing number k equals A005418(k-2). - Andrey Zabolotskiy, May 23 2017

Examples

			a(1) = 2 because 2 is the Conway notation for the Hopf link.
a(2) = 4 because 4 is the Conway notation for the (2,4) torus link.
		

References

• C. Cerf, Atlas of oriented knots and links, Topology Atlas 3 no.2 (1998).
• Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p.210.

Links

• J. H. Conway, An enumeration of knots and links and some of their algebraic properties, 1970. Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) pp. 329-358 Pergamon, Oxford.
• C. Giller, A family of links and the Conway calculus, Trans. American Math Soc., 270 (1982) 75-109.
• Index entries for sequences related to knots

Crossrefs

Cf. A002863, A002864, A018240, A090597, A122495.

Extensions

Sequence edited and more terms added by Andrey Zabolotskiy, May 23 2017