## 52 Citations

### A Spin Analogue of Kerov Polynomials

- Mathematics
- 2018

Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov…

### A positivity conjecture for Jack polynomials

- Mathematics
- 2007

We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the…

### Top degree of Jack characters and enumeration of maps

- Mathematics
- 2015

Jack characters are (suitably normalized) coefficients in the expansion of Jack symmetric functions in the basis of power-sum symmetric functions. These quantities have been introduced recently by…

### On Kerov polynomials for Jack characters

- Mathematics
- 2012

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects,…

### On Kerov polynomials for Jack characters (extended abstract)

- Mathematics
- 2013

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects,…

### Dual combinatorics of zonal polynomials

- Mathematics
- 2011

In this paper we establish a new combinatorial formula for zonal polynomials in terms of power-sums. The proof relies on the sign-reversing involution principle. We deduce from it formulas for zonal…

### Jucys–Murphy elements, orthogonal matrix integrals, and Jack measures

- Mathematics
- 2011

We study symmetric polynomials whose variables are odd-numbered Jucys–Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the…

### Moments of the eigenvalue densities and of the secular coefficients of β-ensembles

- Mathematics
- 2015

We compute explicit formulae for the moments of the densities of the eigenvalues of the classical β-ensembles for finite matrix dimension as well as the expectation values of the coefficients of the…

## References

SHOWING 1-10 OF 28 REFERENCES

### Jack polynomials and some identities for partitions

- Mathematics
- 2003

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted…

### Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations

- Mathematics
- 2010

### A positivity conjecture for Jack polynomials

- Mathematics
- 2007

We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the…

### A recursion and a combinatorial formula for Jack polynomials

- Mathematics
- 1996

Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating…

### An explicit form for Kerov's character polynomials

- Mathematics
- 2005

Kerov considered the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as a polynomial in free cumulants. Biane has proved that this polynomial has…

### Combinatorial interpretation and positivity of Kerov’s character polynomials

- Mathematics
- 2007

Kerov’s polynomials give irreducible character values in terms of the free cumulants of the associated Young diagram. We prove in this article a positivity result on their coefficients, which extends…

### (Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula

- MathematicsCompositio Mathematica
- 1998

We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We strengthen some theorems of F. Knop and S. Sahi and give two explicit formulas for…

### Characters of symmetric groups and free cumulants

- Mathematics
- 2003

We investigate Kerov’s formula expressing the normalized irreducible characters of symmetric groups evaluated on a cycle, in terms of the free cumulants of the associated Young diagrams.

### Character Polynomials and Lagrange Inversion

- Mathematics
- 2005

In this thesis, we investigate two expressions for symmetric group characters: Kerov’s universal character polynomials and Stanley’s character polynomials. We give a new explicit form for Kerov’s…