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Zbl 1064.05021
Yee, Ae Ja
Partitions with difference conditions and Alder's conjecture. (English)
[J] Proc. Natl. Acad. Sci. USA 101, No. 47, 16417-16418 (2004). ISSN 0027-8424; ISSN 1091-6490/e

Summary: In 1956, {\it H. L. Alder} [Research Problem 4, Bull. Am. Math. Soc. 62 (1956), p. 76] 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 $\pm 1\pmod {d+3}$ for $d\ge 4$. In 1971, {\it G. E. Andrews} [Pac. J. Math. 36, 279--284 (1971; Zbl 0195.31201)] proved that the conjecture holds for $d= 2^r-1$, $r\ge 4$. We sketch a proof of the conjecture for all $d\ge 32$.

MSC 2000:: *05A17 Partitions of integres (combinatorics)
11P81 Elementary theory of partitions

Citations: Zbl 0195.31201

Cited in: Zbl 1221.11205

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