Displaying similar documents to “Overpartition pairs”

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...

Permuting the partitions of a prime

Stéphane Vinatier (2009)

Journal de Théorie des Nombres de Bordeaux

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Given an odd prime number p , we characterize the partitions ℓ ̲ of p with p parts ℓ 0 ≥ ℓ 1 ≥ ... ≥ ℓ p - 1 ≥ 0 for which there exist permutations σ , τ of the set { 0 , ... , p - 1 } such that p divides ∑ i = 0 p - 1 i ℓ σ ( i ) but does not divide ∑ i = 0 p - 1 i ℓ τ ( i ) . This happens if and only if the maximal number of equal parts of ℓ ̲ is less than p - 2 . The question appeared when dealing with sums of p -th powers of resolvents, in order to solve a Galois module structure problem.

M 2 -rank differences for partitions without repeated odd parts

Jeremy Lovejoy, Robert Osburn (2009)

Journal de Théorie des Nombres de Bordeaux

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We prove formulas for the generating functions for M 2 -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.