combinatorics, the Stanley symmetric functions are a family of symmetric functions introduced by Richard Stanley (1984) in his study of the symmetric group of permutations...

The chromatic symmetric function is a symmetric function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight...

important role in the representation theory of the symmetric group. The ring of symmetric functions can be given a coproduct and a bilinear form making...

polynomial is a square root of the discriminant. Symmetric function Newton's identities Stanley symmetric function Muirhead's inequality Lang, Serge (2002),...

algebra, the complete homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a...

the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be...

countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric...

the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with...

Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete...

Thomas; Shimozono, Mark (2006). "A Little Bijection for Affine Stanley Symmetric Functions" (PDF). Séminaire Lotharingien de Combinatoire. 54A: B54Ai. arXiv:math...

classified by how symmetric they are. Many symmetric classes of plane partitions are enumerated by simple product formulas. The generating function for PL(n)...

Spike-timing-dependent plasticity | Graph theory | Partially ordered set | Stanley symmetric function | Neural coding | In 2025 the Mendoza-Cortés group released an...

potential applications, from symmetric function theory to quantum chemistry studies of atoms, molecules and solids. The symmetric group Sn has order n!. Its...

give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of...

were introduced by the mathematician Carl Kostka in his study of symmetric functions (Kostka (1882)). For example, if λ = ( 3 , 2 ) {\displaystyle \lambda...

where I {\displaystyle I} is the ideal generated by homogeneous symmetric functions of positive degree. The Schubert polynomial S w {\displaystyle {\mathfrak...

1}}=66528.} A representation of the symmetric group on n elements, Sn is also a representation of the symmetric group on n − 1 elements, Sn−1. However...

Majority function Material conditional Minimal axioms for Boolean algebra Peirce arrow Read-once function Sheffer stroke Sole sufficient operator Symmetric Boolean...

Stanley Kubrick (/ˈkuːbrɪk/; July 26, 1928 – March 7, 1999) was an American filmmaker and photographer. Widely considered one of the greatest filmmakers...

branches of mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representation theory in general. The...

commutative algebra are commonly used. The ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes...

known to Freeman Dyson. His 1979 book Symmetric Functions and Hall Polynomials has become a classic. Symmetric functions are an old theory, part of the theory...

Zhang, Yifeng (March 2022). "Affine transitions for involution Stanley symmetric functions". European Journal of Combinatorics. 101: 103463. arXiv:1812...

Patashnik 1994, §7.4 on special sequence generating functions. Good, I. J. (1986). "On applications of symmetric Dirichlet distributions and their mixtures to...

mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric polynomial which...

permutations Stanley–Wilf conjecture Symmetric function Szymanski's conjecture Twelvefold way Alternating group Automorphisms of the symmetric and alternating...

Lambert W function. The transcendental equation that appears in the determination of the propagation wave number of an electromagnetic axially symmetric surface...

which encode the representations of the symmetric groups, and are connected to the ring of symmetric functions; Okada (1994) defined algebras whose representation...

1960. Sagan, Bruce (2001). The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition. Springer-Verlag. ISBN 0-387-95067-2...

Compared to symmetric cryptography, public-key cryptography can be too slow for many purposes, so these protocols often combine symmetric cryptography...