Yee, Ae Ja Partitions with difference conditions and Alder’s conjecture. (English) Zbl 1064.05021 Proc. Natl. Acad. Sci. USA 101, No. 47, 16417-16418 (2004). Summary: In 1956, 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 \(d\geq 4\). In 1971, G. E. Andrews [Pac. J. Math. 36, 279–284 (1971; Zbl 0195.31201)] proved that the conjecture holds for \(d= 2^r-1\), \(r\geq 4\). We sketch a proof of the conjecture for all \(d\geq 32\). Cited in 1 ReviewCited in 6 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 11P81 Elementary theory of partitions Citations:Zbl 0195.31201 PDFBibTeX XMLCite \textit{A. J. Yee}, Proc. Natl. Acad. Sci. USA 101, No. 47, 16417--16418 (2004; Zbl 1064.05021) Full Text: DOI Digital Library of Mathematical Functions: §26.10(iv) Identities ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis References: [1] BULL AM MATH SOC 62 pp 76– (1956) · doi:10.1090/S0002-9904-1956-09993-8 [2] PACIFIC J MATH 36 pp 279– (1971) · Zbl 0195.31201 · doi:10.2140/pjm.1971.36.279 [3] AM J MATH 91 pp 18– (1969) · Zbl 0186.30203 · doi:10.2307/2373264 [4] BULL AM MATH SOC 54 pp 712– (1948) · Zbl 0035.31201 · doi:10.1090/S0002-9904-1948-09062-0 [5] BULL AM MATH SOC 52 pp 538– (1946) · Zbl 0060.10101 · doi:10.1090/S0002-9904-1946-08605-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.