Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characters of symmetric groups in terms of free cumulants and Frobenius
  coordinates   Free cumulants are nice and useful functionals of the shape of a Young
diagram, in particular they give the asymptotics of normalized characters of
symmetric groups S(n) in the limit n\to\infty. We give an explicit
combinatorial formula for normalized characters of the symmetric groups in
terms of free cumulants. We also express characters in terms of Frobenius
coordinates. Our formulas involve counting certain factorizations of a given
permutation. The main tool are Stanley polynomials which give values of
characters on multirectangular Young diagrams.
  R\'esum\'e. Les cumulants libres sont des fonctions agr\'eables et utiles sur
l'ensemble des diagrammes de Young, en particulier, ils donnent le comportement
asymptotiques des caract\`eres normalis\'es du groupe sym\'etrique S(n) dans la
limite n\to\infty. Nous donnons une formule combinatoire explicite pour les
caract\`eres normalis\'es du groupe sym\'etrique en fonction des cumulants
libres. Nous exprimons \'egalement les caract\`eres en fonction des
coordonn\'ees de Frobenius. Nos formules font intervenir le nombre de certaines
factorisations d'une permutation donn\'ee. L'outil principal est la famille de
polyn\^omes de Stanley donnant les valeurs des caract\`eres sur les diagrammes
de Young multirectangulaires.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph