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.
|Original language||English (US)|
|Number of pages||2|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - Nov 23 2004|
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