相关论文: An explicit form for Kerov's character polynomials

Kerov's polynomials give irreducible character values in term of the free cumulants of the associated Young diagram. We prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Our method,…

Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the free cumulants of the associated Young diagram. We present two positivity conjectures for…

We find an explicit combinatorial interpretation of the coefficients of Kerov character polynomials which express the value of normalized irreducible characters of the symmetric groups S(n) in terms of free cumulants R_2,R_3,... of the…

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 polynomials in spin (or projective)…

We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the…

We prove a formula expressing the Kerov polynomial $\Sigma_k$ as a weighted sum over the lattice of noncrossing partitions of the set $\{1,...,k+1\}$. In particular, such a formula is related to a partial order $\mirr$ on the Lehner's…

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, suggesting some underlying combinatorics. We…

We give a simple proof of an explicit formula for Kerov polynomials. This formula is closely related to a formula of Goulden and Rattan.

Stanley introduced expressions for the normalized characters of the symmetric group and stated some positivity conjectures for these expressions. Here, we give an affirmative partial answer to Stanley's positivity conjectures about the…

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 polynomial in the lengths of the sides of…

The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity,…

We study zonal characters which are defined as suitably normalized coefficients in the expansion of zonal polynomials in terms of power-sum symmetric functions. We show that the zonal characters, just like the characters of the symmetric…

In previous work Regev used part of the representation theory of Lie superalgebras to compute the values of a character of the symmetric group whose decomposition into irreducible constituents is described by semistandard…

The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…

We characterize compatible families of real-rooted polynomials, allowing both positive and negative leading coefficients. Our characterization naturally generalizes the same-sign characterization used by Chudnovsky and Seymour in their…

In this paper, we study relationships between the normalized characters of symmetric groups and the Boolean cumulants of Young diagrams. Specifically, we show that each normalized character is a polynomial of twisted Boolean cumulants with…

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

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 characters evaluated on a strict partition $\xi$…

The principal character of a representation of the free group of rank two into PSL(2, C) is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of…

We introduce a multivariate generalization of normalized Chebyshev polynomials of the second kind. We prove that these polynomials arise in the context of cluster characters associated to Dynkin quivers of type $\mathbb A$ and…