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Jack polynomials and some identities for partitions


Author: Michel Lassalle
Journal: Trans. Amer. Math. Soc. 356 (2004), 3455-3476
MSC (2000): Primary 05A10, 05A17, 05E05, 33C52, 33C80
DOI: https://doi.org/10.1090/S0002-9947-04-03500-7
Published electronically: April 16, 2004
MathSciNet review: 2055741
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Abstract: We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack polynomials. These quantities are the moments of the ``$\alpha$-content'' random variable with respect to some transition probability distributions.


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Additional Information

Michel Lassalle
Affiliation: Centre National de la Recherche Scientifique, Institut Gaspard Monge, Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex, France
Email: lassalle@univ-mlv.fr

DOI: https://doi.org/10.1090/S0002-9947-04-03500-7
Keywords: Partitions, (shifted) symmetric functions, (shifted) Jack polynomials, transition probabilities
Received by editor(s): February 2, 2003
Published electronically: April 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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