Combinatorial interpretation and positivity of Kerov's character polynomials

DOI10.1007/s10801-008-0147-yzbMath1226.05258arXiv0710.5885OpenAlexW2060870403MaRDI QIDQ842856

Valentin Féray

Publication date: 25 September 2009

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.5885

zbMATH Keywords

mapsrepresentationssymmetric group

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10)

Related Items (15)

Gaussian fluctuations of Young diagrams and structure constants of Jack characters ⋮ Cyclic Inclusion-Exclusion ⋮ A spin analogue of Kerov polynomials ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Explicit formulae for Kerov polynomials ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Normalized characters of symmetric groups and Boolean cumulants via Khovanov's Heisenberg category ⋮ Quadratic coefficients of Goulden-Rattan character polynomials ⋮ Zonal polynomials via Stanley's coordinates and free cumulants ⋮ Two positivity conjectures for Kerov polynomials ⋮ Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Unnamed Item ⋮ Jack polynomials and free cumulants ⋮ Quasi-symmetric functions as polynomial functions on Young diagrams

Cites Work

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• Asymptotics of characters of symmetric groups related to Stanley character formula
• Two positivity conjectures for Kerov polynomials
• The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group
• Representations of symmetric groups and free probability
• The asymptotics of interlacing sequences and the growth of continual Young diagrams
• Some properties of crossings and partitions
• Irreducible symmetric group characters of rectangular shape.
• 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
• An explicit form for Kerov's character polynomials

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