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

22 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

Access to Document

10.1515/CRELLE.2008.018

Cite this

@article{049cb5df3f444d0492181bf95571a2b5,

title = "Alder's conjecture",

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.",

author = "Yee, \{Ae Ja\}",

year = "2008",

month = mar,

doi = "10.1515/CRELLE.2008.018",

language = "English (US)",

pages = "67--88",

journal = "Journal fur die Reine und Angewandte Mathematik",

issn = "0075-4102",

publisher = "Walter de Gruyter GmbH",

number = "616",

}

TY - JOUR

T1 - Alder's conjecture

AU - Yee, Ae Ja

PY - 2008/3

Y1 - 2008/3

N2 - 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.

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). 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.

UR - https://www.scopus.com/pages/publications/44949173996

UR - https://www.scopus.com/pages/publications/44949173996#tab=citedBy

U2 - 10.1515/CRELLE.2008.018

DO - 10.1515/CRELLE.2008.018

M3 - Article

AN - SCOPUS:44949173996

SN - 0075-4102

SP - 67

EP - 88

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

IS - 616

ER -

Alder's conjecture

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this