"S-polynomial" redirects here. For the polynomials used in computing Gröbner bases, see Gröbner basis § S-polynomial. For the stable polynomials in discrete-time systems, see Stable polynomial.
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur polynomials form a linear basis for the space of all symmetric polynomials. Any product of Schur polynomials can be written as a linear combination of Schur polynomials with non-negative integral coefficients; the values of these coefficients is given combinatorially by the Littlewood–Richardson rule. More generally, skew Schur polynomials are associated with pairs of partitions and have similar properties to Schur polynomials.
In mathematics, Schurpolynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the...
A polynomial with the first property is called at times a Hurwitz polynomial and with the second property a Schurpolynomial. Stable polynomials arise...
a polynomial. In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schurpolynomials play...
Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric polynomial which generalizes the Schur and zonal polynomials, and...
homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete...
mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one...
algebraic form Schurpolynomial Symbol of a differential operator However, as some authors do not make a clear distinction between a polynomial and its associated...
number of semi-standard Young tableaux, which is a specialization of a Schurpolynomial. Let λ = ( λ 1 ≥ ⋯ ≥ λ k ) {\displaystyle \lambda =(\lambda _{1}\geq...
mathematics, the Schur algorithm may be: The Schur algorithm for expanding a function in the Schur class as a continued fraction The Lehmer–Schur algorithm for...
Companion matrix § Diagonalizability Schurpolynomial – a generalization Alternant matrix Lagrange polynomial Wronskian List of matrices Moore determinant...
A Schur function may be: A Schurpolynomial A holomorphic function in the Schur class This disambiguation page lists mathematics articles associated with...
In mathematics, Schubert polynomials are generalizations of Schurpolynomials that represent cohomology classes of Schubert cycles in flag varieties. They...
mathematics, especially in the field of representation theory, Schur functors (named after Issai Schur) are certain functors from the category of modules over...
polynomials, complete homogeneous symmetric polynomials, and Schurpolynomials. Most relations between symmetric polynomials do not depend on the number n of indeterminates...
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...
one-variable specializations of the Kostka polynomials can be used to relate Hall-Littlewood polynomials Pμ to Schurpolynomials sλ: s λ ( x 1 , … , x n ) = ∑ μ...
f is the composition of Dickson polynomials, degree-one polynomials, and polynomials of the form xk. In fact, Schur did not make any conjecture in this...
function in dim(V) variables, known as the Schurpolynomial sλ corresponding to the Young diagram λ. Schurpolynomials form a basis in the space of symmetric...
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