# 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.

**15**

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

**4**

**1**answer

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

**6**

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### An Ehrhart positivity question related to Schur polynomials

**12**

**1**answer

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

**6**

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

**3**

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### Shifted schur function and holonomic

**9**

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### A binomial determinant formula: a new variant

**13**

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

**2**

**1**answer

### Frobenius coordinate expansion of character

**1**

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### Diagonal operator and infinite wedge space formalism

**7**

**1**answer

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

**1**

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

**1**

**1**answer

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

**3**

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### Bounds related to Monomial Symmetric Functions

**0**

**2**answers

### A symmetric polynomial inequality

**4**

**2**answers

### Combination power elementary symmetric polynomial inequality

**3**

**1**answer

### A generalization of Newton-Girard Identities

**2**

**0**answers

### Quasi-symmetric functions and determinants

**7**

**1**answer

### A Muirhead Like Inequality

**2**

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### An inequality related to Power sum and elementary symmetric polynomial and majorizes

**6**

**0**answers

### Decomposition of even symmetric polynomials and Euler numbers

**13**

**1**answer

### Character theoretic proof of the Littlewood–Richardson rule?

**6**

**0**answers

### Expansion of elementary symmetric function in Jack's?

**4**

**1**answer

### Quasi-symmetric generalizations of classical symmetric functions

**5**

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### Explicit form of raising and lowering operators in spherical gl(n) DAHA

**0**

**4**answers

### Show that sets are equal

**1**

**1**answer

### On two types of shifted symmetric power sums

**5**

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### Interpretation of Hilbert/Frobenius series shift

**39**

**3**answers

### Characterizing positivity of formal group laws

**0**

**0**answers

### Methods to get Holonomic functions

**4**

**1**answer

### Symmetric functions of eigenvalues

**4**

**1**answer

### Decompostion of hook schur function in terms of cauchy product of holonomic functions

**2**

**1**answer

### Generalized Newton Identities

**7**

**0**answers

### Characterizing $n$-exceptions of the ring of symmetric polynomials

**3**

**2**answers

### Bounded Degree in Ring of Symmetric Functions

**14**

**1**answer

### Inequalities on elementary symmetric polynomials

**6**

**0**answers

### Natural maps between Schur functors: understanding the image

**1**

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### Holonomic generating function

**6**

**1**answer

### Rational generating function and recursion

**5**

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### Internal tensor product of strict polynomial functors: is there a more explicit definition?

**12**

**1**answer

### What is currently known or conjectured about q,t-Kostka polynomials?

**1**

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### Hook-content polynomial 2

**3**

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### Hook-content polynomial

**14**

**3**answers

### Schubert calculus expressed in terms of the cotangent space of the Grassmannians

**2**

**0**answers

### Partial Flag Varieties and Quotients of Symmetric Polynomials

**3**

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### Product of Schur functions

**24**

**5**answers

### Understanding a quip from Gian-Carlo Rota

**1**

**1**answer

### Cauchy identity, with sum restricted over partitions with first part $\leq n$

**10**

**1**answer

### Cauchy identity in three sets of variables?

**7**

**1**answer