Partitions with difference conditions and Alder's conjecture

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Abstract

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 languageEnglish (US)
Pages (from-to)16417-16418
Number of pages2
JournalProceedings of the National Academy of Sciences of the United States of America
Volume101
Issue number47
DOIs
StatePublished - Nov 23 2004

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