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 equivalent to +/-1 (mod d + 3) for d greater than or equal to 4. In 1971, Andrews proved that the conjecture holds for d = 2(r) - 1, r greater than or equal to 4. We sketch a proof of the conjecture for all d greater than or equal to 32.
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机译：1956年，Alder推测n划分成至少相差d的部分的分隔数量大于或等于n划分成等于+/- 1（mod d + 3）的部分的数量，其中d大于或等于到4。1971年，安德鲁斯证明d = 2（r）-1，r大于或等于4的猜想成立。我们对所有d大于或等于32的猜想进行证明。
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