Partitions with difference conditions and Alder's conjecture.
Partitions with difference conditions and Alder's conjecture.
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DOI：
10.1073/pnas.0406971101
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发表时间：
2004-11
影响因子：
11.1
通讯作者：
A. Yee
中科院分区：
文献类型：
--
作者：
A. Yee
在1956年，桤木证明了n分成至少相差d的部分的数目大于或等于n分成与+/-1（mod d+3）相同的部分的数目，其中d >或= 4。1971年，安德鲁斯证明了这个猜想对d = 2 r-1，r ≥ 4成立。我们对所有d >或= 32的猜想给出一个证明。
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 identical with +/-1 (mod d+3) for d > or = 4. In 1971, Andrews proved that the conjecture holds for d = 2r-1, r > or = 4. We sketch a proof of the conjecture for all d > or = 32.