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

1,1

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

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

Table of n, a(n) for n=1..29.

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

Example

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.

Crossrefs

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

Sequence in context: A068479 A116010 A018677 * A111355 A018706 A111162

Adjacent sequences: A173634 A173635 A173636 * A173638 A173639 A173640

Keyword

nonn

Author

Jonathan Vos Post, Nov 23 2010

Extensions

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

Status

approved