TY - JOUR
T1 - Partitions with difference conditions and Alder's conjecture
AU - Yee, Ae Ja
PY - 2004/11/23
Y1 - 2004/11/23
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) 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.
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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U2 - 10.1073/pnas.0406971101
DO - 10.1073/pnas.0406971101
M3 - Article
C2 - 15546985
AN - SCOPUS:9344244735
SN - 0027-8424
VL - 101
SP - 16417
EP - 16418
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 47
ER -