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Motivated by classical identities of Euler, Schur, and Rogers and Ramanujan, Alder investigated qd(n) and Qd(n), the number of partitions of n into d-distinct parts and into parts which are ±1(mod d + 3), respectively. He conjectured that qd(n) ≥ Qd(n) Andrews and Yee proved the conjecture for d = 2s −1 and also for d ≥ 32. We complete the proof of Andrews's refinement of Alder's conjecture by ... read moredetermining effective asymptotic estimates for these partition functions (correcting and refining earlier work of Meinardus), thereby reducing the conjecture to a finite computation. (c) 2010 American Mathematical Society.read less
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