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An operation on a knot or link diagram which preserves its crossing number. Thistlethwaite used 13 different moves in generating a list of 16-crossing alternating knots ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...

The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

A knot diagram which does not specify whether crossings are under- or overcrossings.

The signature s(K) of a knot K can be defined using the skein relationship s(unknot)=0 (1) s(K_+)-s(K_-) in {0,2}, (2) and 4|s(K)<->del (K)(2i)>0, (3) where del (K) is the ...

Two oriented knots (or links) can be summed by placing them side by side and joining them by straight bars so that orientation is preserved in the sum. The knot sum is also ...

A symmetry of a knot K is a homeomorphism of R^3 which maps K onto itself. More succinctly, a knot symmetry is a homeomorphism of the pair of spaces (R^3,K). Hoste et al. ...

The mathematical study of knots. Knot theory considers questions such as the following: 1. Given a tangled loop of string, is it really knotted or can it, with enough ...

The Knuth-Bendix completion algorithm attempts to transform a finite set of identities into a finitely terminating, confluent term rewriting system whose reductions preserve ...

The numbers defined by the recurrence relation K_(n+1)=1+min(2K_(|_n/2_|),3K_(|_n/3_|)), with K_0=1. The first few values for n=0, 1, 2, ... are 1, 3, 3, 4, 7, 7, 7, 9, 9, ...