Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Nekrasov-Okounkov hook length formula: refinement, elementary proof,
  extension and applications   The paper is devoted to the derivation of the expansion formula for the
powers of the Euler Product in terms of partition hook lengths, discovered by
Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a
refinement based on a new property of t-cores, and give an elementary proof by
using the Macdonald identities. We also obtain an extension by adding two more
parameters, which appears to be a discrete interpolation between the Macdonald
identities and the generating function for t-cores. Several applications are
derived, including the "marked hook formula".

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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an