the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant...

Randal Jones (31 December 1952 – 6 September 2020) was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was...

Jones discovered the Jones polynomial. This led to the discovery of more knot polynomials, such as the so-called HOMFLY polynomial. Soon after Jones'...

theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant...

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

polynomial ring can be endowed with a structure of a commutative, cocommutative Hopf algebra. Jones polynomial Weisstein, Eric W. "Laurent Polynomial"...

famous knot invariant called the Jones polynomial. The bracket polynomial is important in unifying the Jones polynomial with other quantum invariants. In...

a cochain complex. It may be regarded as a categorification of the Jones polynomial. It was developed in the late 1990s by Mikhail Khovanov. To any link...

realized until the discovery of the Jones polynomial in 1984. Soon after Conway's reworking of the Alexander polynomial, it was realized that a similar skein...

calculate knot invariants and three-manifold invariants such as the Jones polynomial. Particularly, Chern–Simons theory is specified by a choice of simple...

Jones polynomial. A key insight of Michael Freedman in 1997 was to compare Witten's results with the fact that the evaluation of the Jones polynomial...

defining new, powerful knot invariants. The discovery of the Jones polynomial by Vaughan Jones in 1984 (Sossinsky 2002, pp. 71–89), and subsequent contributions...

knot invariant called the Jones polynomial. The bracket polynomial plays an important role in unifying the Jones polynomial with other quantum invariants...

Touchard polynomials Wilkinson's polynomial Wilson polynomials Zernike polynomials Pseudo-Zernike polynomials Alexander polynomial HOMFLY polynomial Jones polynomial...

efficiently computable for this purpose. It is not known whether the Jones polynomial or finite type invariants can detect the unknot. It can be difficult...

particularly simple and common example. Other examples are knot polynomials, such as the Jones polynomial, which are currently among the most useful invariants...

ISBN 0-521-63503-9. Aharonov, D.; Jones, V.; Landau, Z. (2006). "A polynomial quantum algorithm for approximating the Jones polynomial". Proceedings of the 38th...

The Jones polynomial is a special case of the Kauffman polynomial, as the L polynomial specializes to the bracket polynomial. The Kauffman polynomial is...

Vaughan Jones' discovery of the Jones polynomial in 1984. This led to other knot polynomials such as the bracket polynomial, HOMFLY polynomial, and Kauffman...

the Aharonov–Jones–Landau algorithm is an efficient quantum algorithm for obtaining an additive approximation of the Jones polynomial of a given link...

and Morwen Thistlethwaite in 1987, using the Jones polynomial. A geometric proof, not using knot polynomials, was given in 2017 by Joshua Greene. A second...

because of its Conway polynomial, which is ∇ ( z ) = 1 − z 2 ,   {\displaystyle \nabla (z)=1-z^{2},\ } and the Jones polynomial is V ( q ) = q 2 − q +...

categorification of the Jones polynomial" (Page 337). Khovanov, Mikhail (2000), "A categorification of the Jones polynomial", Duke Mathematical Journal...

{\displaystyle 1} . The theory of subfactors led to the discovery of the Jones polynomial in knot theory. Usually M {\displaystyle M} is taken to be a factor...

1 / t ) {\displaystyle V(1/t)} is the Jones polynomial for the mirror image of a link having Jones polynomial V ( t ) {\displaystyle V(t)} . The hyperbolic...

shares the same Jones polynomial. Both knots also have the curious property of having the same Alexander polynomial and Conway polynomial as the unknot...

bewildering profusion of generalizations. He had found a new knot polynomial, the Jones polynomial. Specifically, it is an invariant of an oriented knot or link...

Many important invariants can be defined in this way, including the Jones polynomial. The type I move is the only move that affects the writhe of the diagram...

systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated...

theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability...