Partitions with difference conditions and Alder's conjecture

Ae Ja Yee

doi:10.1073/pnas.0406971101

Partitions with difference conditions and Alder's conjecture

Ae Ja Yee

Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 = 2^r - 1, r ≥ 4. We sketch a proof of the conjecture for all d ≥ 32.

Original language	English (US)
Pages (from-to)	16417-16418
Number of pages	2
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	101
Issue number	47
DOIs	https://doi.org/10.1073/pnas.0406971101
State	Published - Nov 23 2004

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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.",

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AB - 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.

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JF - Proceedings of the National Academy of Sciences of the United States of America

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Partitions with difference conditions and Alder's conjecture

Abstract

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