$M_2$-rank differences for partitions without repeated odd parts

Jeremy Lovejoy; Robert Osburn

Displaying similar documents to “ $M_{2}$ -rank differences for partitions without repeated odd parts”

Hooks and powers of parts in partitions.

Bacher, Roland, Manivel, Laurent (2002)

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Supernomial coefficients, supernomials coefficients Bailey's lemma and Rogers-Ramanujan-type identities. A survey of results and open problems.

Warnaar, S.Ole (1999)

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Qseries Maple tutorial: A $q$ -product tutorial for a $q$ -series Maple package.

Garvan, Frank (1999)

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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 $\underset{̲}{ℓ}$ of $p$ with $p$ parts $ℓ_{0} \geq ℓ_{1} \geq ... \geq ℓ_{p - 1} \geq 0$ for which there exist permutations $σ, τ$ of the set ${0, ..., p - 1}$ such that $p$ divides $\sum_{i = 0}^{p - 1} i ℓ_{σ (i)}$ but does not divide $\sum_{i = 0}^{p - 1} i ℓ_{τ (i)}$ . This happens if and only if the maximal number of equal parts of $\underset{̲}{ℓ}$ 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.

Enumeration of sequences constrained by the ratio of consecutive parts.

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

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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...

Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture.

Langer, Robin, Schlosser, Michael J., Warnaar, S.Ole (2009)

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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.

Displaying similar documents to “ M 2 -rank differences for partitions without repeated odd parts”

Displaying similar documents to “ $M_{2}$ -rank differences for partitions without repeated odd parts”