# Questions tagged [symmetric-functions]

Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.

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### Derivatives of Riemann $\xi$ and traces of zeros

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### Symmetric functions for multidimensional variables

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### Can we extend a function from the diagonal matrices to an orthogonally-invariant function on $\text{GL}_n$?

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### Jack function in power symmetric basis

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### Using irreducible characters of the orthogonal group as basis for homogeneous symmetric polynomials

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### What makes skew characters of the symmetric group special?

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### Multivariate analogue of exponential infinite series

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### Calculation of complete homogeneous symmetric functions [closed]

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### Solutions to a special confluent Vandermonde system

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### Change variable in integration with symmetry

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### Why do we define the hypergeometric function of a matrix argument for symmetric matrices only?

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### Does the hypergeometric function of a matrix argument depend on $\alpha$ for a $1\times 1$ matrix?

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### Applying a simple involution to Hall-Littlewood polynomials

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### look for differentiable symmetric functions whose global minimizer has all distinct components

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### Macdonald's idea of his kth weight

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### Iterated derivative and rectangular standard Young tableaux

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### Decomposing Schur functor applied to a tensor product

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### Pieri-type rule for Schur P-functions

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### $G$-analogues of symmetric functions (reference request)

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### Interpolating Maximum function with symmetric polynomials

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### Is there an example of two graphs with the same Dichromatic Symmetric Function?

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### Extension of definition of Holonomic closure

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### Symmetric function transition matrix and a non-conjecture by Clifford and Stanley

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### Schur function on unit circles

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### Characters of orthogonal groups as symmetric functions

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### The vanishing of sum of coefficients: symmetric polynomials

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### Littlewood-Richardson coefficients for zonal polynomials

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### How to prove this identity on summations and partitions?

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### An inequality on elementary symmetric polynomial of eigenvalues

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### A symmetric function that appears in the coefficients of a power expansion

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### Evaluation of a complete homogeneous symmetric polynomial related to Stirling number of 2nd kind

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### Schur-Weyl duality and q-symmetric functions

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### Optimizing a multivariate symmetric (permutation-invariant) function

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### An Ehrhart positivity question related to Schur polynomials

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### Is there a Giambelli identity with dual representations?

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### Macdonald's “Symmetric Functions and Hall Polynomials” Section 1.5 Example 9

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### Shifted schur function and holonomic

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### A binomial determinant formula: a new variant

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### Generalization of Newton's identities to Schur functions

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### Frobenius coordinate expansion of character

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### Diagonal operator and infinite wedge space formalism

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### Reference for Kakutani result on power sum bases of symmetric functions

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### Necessary conditions for a function to be represented as symmetric tensor product

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### Does stability of equilibrium point preserved by permutation matrix (symmetry)?

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### Bounds related to Monomial Symmetric Functions

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### A symmetric polynomial inequality

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### Combination power elementary symmetric polynomial inequality

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### A generalization of Newton-Girard Identities

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### Quasi-symmetric functions and determinants

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