Partitions with difference conditions and Alder's conjecture.
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.
Yee
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Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. yee@math.psu.edu