## 17 Citations

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,…

Jack polynomials and orientability generating series of maps

- Mathematics
- 2013

We study Jack characters, which are the coefficients of the power-sum expansion of Jack symmetric functions with a suitable normalization. These quantities have been introduced by Lassalle who…

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…

Stanley character polynomials

- Mathematics
- 2014

Stanley considered suitably normalized characters of the symmetric groups on Young diagrams having a special geometric form, namely multirectangular Young diagrams. He proved that the character is a…

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…

Linear versus spin: representation theory of the symmetric groups

- MathematicsAlgebraic Combinatorics
- 2020

We relate the linear asymptotic representation theory of the symmetric groups to its spin counterpart. In particular, we give explicit formulas which express the normalized irreducible spin…

Asymptotic results for Representation Theory

- Mathematics
- 2018

Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises…

Cyclic Inclusion-Exclusion

- MathematicsSIAM J. Discret. Math.
- 2015

This work considers a linear map which associates to an acyclic directed graph (or a poset) a quasi-symmetric function and describes the kernel of this linear map by using a simple combinatorial operation that is called cyclic inclusion-exclusion.

Topological expansion of the coefficients of zonal polynomials in genus one

- Mathematics
- 2011

We use a combinatorial interpretation of the coefficients of zonal Kerov polynomials as a number of unoriented maps to derive an explicit formula for the coefficients in genus one.

## References

SHOWING 1-10 OF 34 REFERENCES

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…

I.—A class of symmetric polynomials with a parameter

- MathematicsProceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences
- 1970

Synopsis In an attempt to evaluate the integral (5) below, using a decomposition of an orthogonal matrix (Jack 1968), the author is led to define a set of polynomials, one for each partition of an…

Representations of Symmetric Groups and Free Probability

- Mathematics
- 1998

Abstract We consider representations of symmetric groupsSqfor largeq. We give the asymptotic behaviour of the characters when the corresponding Young diagrams, rescaled by a factorq−1/2, converge to…

Gaussian fluctuations of characters of symmetric groups and of Young diagrams

- Mathematics
- 2006

We study asymptotics of reducible representations of the symmetric groups Sq for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and…

MAPS IN LOCALLY ORIENTABLE SURFACES, THE DOUBLE COSET ALGEBRA, AND ZONAL POLYNOMIALS

- Mathematics
- 1996

Abstract The genus series is the generating series for the number of maps (inequivalent two-cell embeddings of graphs), in locally orientable surfaces, closed and without boundary, with respect to…

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

- Mathematics
- 2010

Asymptotics of characters of symmetric groups related to Stanley character formula

- Mathematics
- 2011

We prove an upper bound for characters of the symmetric groups. In particular, we show that there exists a constant a > 0 with a property that for every Young diagram with n boxes, r( ) rows and c( )…

The Selberg–Jack Symmetric Functions

- Mathematics
- 1997

Abstract K. Aomoto has recently given a simple proof of an extension of A. Selberg's integral. We prove the following generalization of Aomoto's theorem. For eachk⩾0, there exists a family {skλ(t)}…