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

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dc.creatorHan, Guo-Niu
dc.date2008-05-09
dc.date.accessioned2026-07-07T09:38:04Z
dc.date.available2026-07-07T09:38:04Z
dc.descriptionThe 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".
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0805.1398
dc.identifierhttp://arxiv.org/abs/0805.1398
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160676
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleThe Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
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