Displaying similar documents to “Generalized Frobenius partitions, k-cores, k-quotients, and cranks”

Overpartition pairs

Jeremy Lovejoy (2006)

Annales de l’institut Fourier

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An overpartition pair is a combinatorial object associated with the q -Gauss identity and the 1 ψ 1 summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.

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

Guo-Niu Han (2010)

Annales de l’institut Fourier

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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...

Semiring of Sets

Roland Coghetto (2014)

Formalized Mathematics

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Schmets [22] has developed a measure theory from a generalized notion of a semiring of sets. Goguadze [15] has introduced another generalized notion of semiring of sets and proved that all known properties that semiring have according to the old definitions are preserved. We show that this two notions are almost equivalent. We note that Patriota [20] has defined this quasi-semiring. We propose the formalization of some properties developed by the authors.