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

DOI10.1016/j.aim.2010.02.011zbMath1231.05283arXiv0810.3209OpenAlexW2081476180WikidataQ114211694 ScholiaQ114211694MaRDI QIDQ986075

Piotr Śniady, Valentin Féray, Maciej Dołęga

Publication date: 11 August 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.3209

zbMATH Keywords

representations of symmetric groupsfree cumulantsKerov polynomialsfactorizations of permutations

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10)

Related Items (25)

Bijection between oriented maps and weighted non-oriented maps ⋮ Gaussian fluctuations of Young diagrams and structure constants of Jack characters ⋮ Cyclic Inclusion-Exclusion ⋮ A spin analogue of Kerov polynomials ⋮ New characterization of two-state normal distribution ⋮ The ring of \(\mathcal {T}\)-covariants ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Gaussian fluctuations of Jack-deformed random Young diagrams ⋮ Explicit formulae for Kerov polynomials ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Asymptotics of characters of symmetric groups: structure of Kerov character polynomials ⋮ Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category ⋮ Random matrices associated to Young diagrams ⋮ Quadratic coefficients of Goulden-Rattan character polynomials ⋮ Polynomial splitting measures and cohomology of the pure braid group ⋮ Asymptotics of characters of symmetric groups related to Stanley character formula ⋮ Zonal polynomials via Stanley's coordinates and free cumulants ⋮ Asymptotics of Jack characters ⋮ Partial sum of matrix entries of representations of the symmetric group and its asymptotics ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Random strict partitions and random shifted tableaux ⋮ Linear versus spin: representation theory of the symmetric groups ⋮ Stanley character formula for the spin characters of the symmetric groups ⋮ Jack polynomials and free cumulants ⋮ Quasi-symmetric functions as polynomial functions on Young diagrams

Cites Work

• Asymptotics of characters of symmetric groups related to Stanley character formula
• Stanley's formula for characters of the symmetric group.
• Combinatorial interpretation and positivity of Kerov's character polynomials
• Two positivity conjectures for Kerov polynomials
• Addition of certain non-commuting random variables
• Limit laws for random matrices and free products
• A variational problem for random Young tableaux
• Representations of symmetric groups and free probability
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• Irreducible symmetric group characters of rectangular shape.
• Content evaluation and class symmetric functions
• Upper bound on the characters of the symmetric groups
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula.
• Asymptotics of characters of symmetric groups, genus expansion and free probability.
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• On the formula of Goulden and Rattan for Kerov polynomials
• Free Random Variables
• An explicit form for Kerov's character polynomials
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory
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