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.
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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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