An enumeration of knots and links, and some of their algebraic properties. (English) Zbl 0202.54703

Comput. Probl. abstract Algebra, Proc. Conf. Oxford 1967, 329-358 (1970).
Utilizing a clever method and notation, the author produces an enumeration of all knots with 11 or fewer crossings and all links with 10 or fewer crossings. The author claims that knots or links of 12 or 13 crossings may be handled by the methods by computer. (He compiled his list by hand). Included in this listing are invariants for some but not all the knots. In keeping with the historic tradition of this aspect of knot theory, the author has not included any proofs.
Editorial remark (2021): This enumeration corrects several omissions and duplications in the classical lists of Tait and Little, but misses one identical pair identified later by K. A. Perko jun. [Proc. Am. Math. Soc. 45, 262–266 (1974; Zbl 0256.55004)]. See also [A. Stoimenow, Diagram genus, generators, and applications. Boca Raton, FL: CRC Press (2016; Zbl 1336.57016)].
Reviewer: L. P. Neuwirth