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) for d ≥ 4. In 1971, Andrews proved that the conjecture holds for d = 2r – 1, r ≥ 4. We sketch a proof of the conjecture for all d ≥ 32.
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机译：1956年，Alder猜想，对于d≥4，n分成至少d的部分的划分数目大于或等于into±1（mod d + 3）的n的划分数目。1971年，Andrews证明了d = 2 r – 1，r≥4的猜想成立。我们对所有d≥32的猜想进行证明。
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