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The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications

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arxiv 0805.1398 v1 pith:JUNIHROQ submitted 2008-05-09 math.CO math.RT

classification math.COmath.RT
keywords formulahookapplicationselementaryextensionidentitiesmacdonaldproof
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 5 citations worldwide. Full citation record

  1. On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials

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    Refined asymptotics identify the smallest counterexample to log-concavity of D'Arcais polynomials at λ = 65214507758400 and estimate their asymptotic density.

  2. Quiver superconformal index and giant gravitons: asymptotics and expansions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.

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