# 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.

**1**

**0**answers

### Continuous decomposition of permutation-invariant set functions

**8**

**1**answer

### $2$-adic valuation of Schur $P$-functions in the power-sum basis

**7**

**2**answers

### About the sum of rectangular power sums

**3**

**0**answers

### Multiplicities of irreducible $U(n)$-modules in the tensor product $V_{\lambda}\otimes V_{\mu}$

**3**

**0**answers

### Polynomial invariant relating the circumradius and sides of a cyclic polygon

**1**

**0**answers

### A holonomic function and its singularity

**6**

**0**answers

### Expanding the zonal polynomial $Z_\lambda(x/(1-x))$

**1**

**0**answers

### Maximally independent polynomial families with row symmetry

**3**

**1**answer

### Is there a Jacobi–Trudi formula for skew zonal polynomials?

**3**

**1**answer

### Different ways of defining the Chern character of a complex

**0**

**0**answers

### Can I write this series in a recursive way?

**2**

**1**answer

### Changing $S_2 \wr S_n$ for $S_n \wr S_2$ in the theory of zonal polynomials

**4**

**0**answers

### This sum over partitions has unexpectedly nice denominators

**15**

**1**answer

### a Vandermonde-type of determinants summed over permutations

**8**

**0**answers

### Two majs for standard Young tableaux?

**4**

**1**answer

### proof of result from Ian Macdonald's paper "A New Class of Symmetric Functions"

**6**

**1**answer

### Typo in Stanley, Enumerative combinatorics II, Cor. 7.23.9?

**1**

**1**answer

### Are top Brauer characters bounded?

**5**

**0**answers

### Form on symmetric functions and their q,t- analogues

**2**

**0**answers

### Double Schur function expansion

**12**

**1**answer

### Recognizing algebraic independence among Schur polynomials

**5**

**1**answer

### "Kronecker Product" for quasi-symmetric functions

**10**

**1**answer

### Todd polynomials

**3**

**0**answers

### Can equality of chromatic symmetric functions of two trees be checked in polynomial time?

**15**

**1**answer

### A formula for this generating function that is similar to the $qt$-Catalan numbers

**2**

**1**answer

### A doubt in the proof of theorem regarding chromatic symmetric functions

**2**

**0**answers

### Question regarding elementary symmetric functions

**5**

**0**answers

### A conjecture about sums over partitions arising from Hilbert scheme of points

**10**

**1**answer

### Generalization of symmetric functions

**6**

**0**answers

### Derivations for symmetric functions

**1**

**1**answer

### Combinatorics and geometry underlying a refined Pascal matrix/Newton identities

**8**

**1**answer

### Interaction of plethysm with other operations

**1**

**0**answers

### Quick ways to compute transition matrices for classical symmetric function bases

**5**

**1**answer

### On a certain expansion in term of Schur functions

**1**

**0**answers

### Conjugation of bosonic and fermionic

**2**

**0**answers

### Cut and Join for Hurwitz number with multiple spin

**0**

**0**answers

### Generalization of elementary symmetric polynomials

**1**

**1**answer

### On the value of a skew Schur function at the identity

**3**

**0**answers

### Is there an analog of polarization for skew-symmetric forms?

**5**

**0**answers

### Expressing the elementary symmetric polynomials in the $(x_i-x_j)^2$ variables in term of the elementary polynomials in the $x_k$ variables

**3**

**0**answers

### Subalgebras of a polynomial ring carved out by (families of) coefficient equalities

**3**

**1**answer

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

**1**

**0**answers

### Symmetric functions for multidimensional variables

**0**

**0**answers

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

**5**

**1**answer

### Jack function in power symmetric basis

**10**

**2**answers

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

**7**

**2**answers

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

**1**

**0**answers

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

**3**

**0**answers

### Solutions to a special confluent Vandermonde system

**1**

**0**answers