Jack polynomials and some identities for partitions

DOI10.1090/S0002-9947-04-03500-7zbMath1043.05005arXivmath/0306222MaRDI QIDQ4813814

Michel Lassalle

Publication date: 13 August 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306222

zbMATH Keywords

generating functionsymmetric functionsprobability distributionsJack polynomialsrandom variablecombinatorial coefficients

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial aspects of partitions of integers (05A17) Symmetric functions and generalizations (05E05) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items

Random walks generated by the Ewens distribution on the symmetric group, Superconformal blocks in diverse dimensions and \textit{BC} symmetric functions, Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures, Contents of partitions and the combinatorics of permutation factorizations in genus $0$, An explicit formula for the characters of the symmetric group., Two new families of \(q\)-positive integers, Martingales and character ratios, Jack polynomials and free cumulants

Uses Software

• ACE

Cites Work

• Generalized binomial coefficients and Macdonald polynomials
• Some combinatorial conjectures regarding the classical Chu- Vandermonde formula
• Some combinatorial conjectures for Jack polynomials
• Some combinatorial conjectures for shifted Jack polynomials
• Plethystic formulas for Macdonald \(q,t\)-Kostka coefficients
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• Shifted Jack polynomials, binomial formula, and applications
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• A new family of positive integers
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• A remarkable identity in the theory of partitions
• Generalization of Waring-type formulas
• Some combinatorial properties of Jack symmetric functions
• On a generalization of binomial coefficients
• An identity in the theory of partitions
• Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
• Random Young tableaux and combinatorial identities
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