field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram....

in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. It is related by mutation to...

modified multiplication operation Mutation (knot theory), an operation on a knot that creates different knots Mutation (Jordan algebra), an operation on...

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope,...

Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs...

(June 2000). "On the Kinoshita-Terasaka knot and generalised Conway mutation" (PDF). Journal of Knot Theory and Its Ramifications. 09 (4): 557–575. doi:10...

In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus...

In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two...

mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence...

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot...

In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other...

In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest...

In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism...

In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the...

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies...

In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one...

In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square...

moves (I. twist move, II. poke move, and III. slide move). Knot sum Murasugi sum Mutation (knot theory) Weisstein, Eric W. "Knot Move". MathWorld. v t e...

mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. By way...

In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number...

of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. The...

In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related...

field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent...

In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot...

Bridge number 2 In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given...

In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop...

Silent mutations, also called synonymous or samesense mutations, are mutations in DNA that do not have an observable effect on the organism's phenotype...

The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan...

mathematics that studies knots is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional...

In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is...