### Enumeration of sequences constrained by the ratio of consecutive parts.

Corteel, Sylvie, Lee, Sunyoung, Savage, Carla D. (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

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Corteel, Sylvie, Lee, Sunyoung, Savage, Carla D. (2005)

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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...

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