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Alder's conjecture
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Ae Ja Yee
Published/Copyright:
May 13, 2008
Abstract
In 1956, Alder conjectured that the number of partitions of n into parts differing by at least d is greater than or equal to that of partitions of n into parts ≡ ±1 (mod d + 3). The Euler identity, the first Rogers-Ramanujan identity, and a theorem of Schur show that the conjecture is true for d = 1, 2, 3, respectively. In 1971, Andrews proved that the conjecture holds for d = 2r – 1, r ≧ 4. In this paper, we prove the conjecture for all d ≧ 32 and d = 7.
Received: 2005-04-13
Revised: 2006-12-26
Published Online: 2008-05-13
Published in Print: 2008-March
© Walter de Gruyter
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Articles in the same Issue
- Smooth localized parametric resonance for wave equations
- Estimates and regularity results for the DiPerna-Lions flow
- Sur le nombre d'éléments exceptionnels d'une base additive
- Alder's conjecture
- Local monotonicity and mean value formulas for evolving Riemannian manifolds
- Projective-injective modules, Serre functors and symmetric algebras
- Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
- Zeros of complex caloric functions and singularities of complex viscous Burgers equation
- Generalised form of a conjecture of Jacquet and a local consequence
