Alder's conjecture

Ae Ja Yee

doi:10.1515/CRELLE.2008.018

Alder's conjecture

Ae Ja Yee

Mathematics

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

18 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). The Euler identity, the first Rogers-Ramanujan identity, and a theorem of Schur show that the conjecture is true for d = 1, 2, 3, respectively. In 1971, Andrews proved that the conjecture holds for d = 2^r - 1, r ≧ 4. In this paper, we prove the conjecture for all d ≧ 32 and d = 7.

Original language	English (US)
Pages (from-to)	67-88
Number of pages	22
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	616
DOIs	https://doi.org/10.1515/CRELLE.2008.018
State	Published - Mar 2008

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2008.018

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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). The Euler identity, the first Rogers-Ramanujan identity, and a theorem of Schur show that the conjecture is true for d = 1, 2, 3, respectively. In 1971, Andrews proved that the conjecture holds for d = 2r - 1, r ≧ 4. In this paper, we prove the conjecture for all d ≧ 32 and d = 7.",

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Alder's conjecture

Abstract

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