mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links. Although it...

bracket polynomial is a Laurent polynomial in the variable A {\displaystyle A} with integer coefficients. First, we define the auxiliary polynomial (also...

knots in knot polynomials. Alexander polynomial Bracket polynomial HOMFLY polynomial Jones polynomial Kauffman polynomial Graph polynomial, a similar class...

coefficient Bracket polynomial Bra-ket notation Delimiter Dyck language Frölicher–Nijenhuis bracket Iverson bracket Nijenhuis–Richardson bracket, also known...

best known for the introduction and development of the bracket polynomial and the Kauffman polynomial. Kauffman was valedictorian of his graduating class...

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

the function by a polynomial of low degree, which takes the same values at these approximate roots. Then the root of the polynomial is computed and used...

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander...

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

bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation. The method is applicable for numerically solving...

In mathematics and computer science, polynomial evaluation refers to computation of the value of a polynomial when its indeterminates are substituted for...

solutions, similarly as polynomial algebras are used for the study of algebraic varieties, which are solution sets of systems of polynomial equations. Weyl algebras...

orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...

the Jones polynomial in 1984. This led to other knot polynomials such as the bracket polynomial, HOMFLY polynomial, and Kauffman polynomial. Jones was...

In mathematics, Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. They are named after François Viète (1540-1603)...

the bracket ring is the subring of the ring of polynomials k[x11,...,xdn] generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring...

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 diagram...

\{\{x\}\}} of the variable in the circle group occur, under the name "bracket polynomials". Since the theory is in the setting of Lipschitz functions, which...

result now is obtained by writing the same polynomial of degree four as a Poisson bracket of polynomials of degree three in two different ways. Specifically...

{\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket, an alternating bilinear map g × g → g {\displaystyle {\mathfrak {g}}\times...

factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a polynomial, then x − a {\displaystyle...

conditions for polynomials in derivatives of modular forms to be modular forms, and Cohen (1975) found the explicit examples of such polynomials that give...

Jones polynomial. Also known as the Kauffman bracket. Conway polynomial uses Skein relations. Homfly polynomial or HOMFLYPT polynomial. Jones polynomial assigns...

{p_{n-1}(x)}{a_{n-1}}}\right)+{\frac {p_{n-1}(x)}{a_{n-1}}}} The term in the brackets is a polynomial of degree n − 2 {\displaystyle n-2} , which is therefore orthogonal...

algebra S(V) can be identified, through a canonical isomorphism, to the polynomial ring K[B], where the elements of B are considered as indeterminates. Therefore...

Zhegalkin (also Žegalkin, Gégalkine or Shegalkin) polynomials (Russian: полиномы Жегалкина), also known as algebraic normal form, are a representation...

In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987...

operations, and functions. Other symbols include punctuation marks and brackets, used for grouping where there is not a well-defined order of operations...

Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian polynomials, or q-binomial coefficients) are q-analogs of the binomial coefficients...

{\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis. Other notations...