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A composite knot is a knot that is not a prime knot. Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

Let R^3 be the space in which a knot K sits. Then the space "around" the knot, i.e., everything but the knot itself, is denoted R^3-K and is called the knot complement of K ...

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 which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. ...

The Perko pair is the pair of knots 10_(161) and 10_(162) illustrated above. For many years, they were listed as separate knots in Little (1885) and all similar tables, ...

A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any ...

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a ...

A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even so, such integrals can converge, in ...