A theorem of Andrews equates partitions in which no part is repeated more than 2k−1 times to partitions in which, if j appears at least k times, all parts less than j also do so. This paper proves the theorem bijectively, with some of the generalizations that usually arise from such proofs.
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Andrews, G.: Partitions with initial repetitions. Acta Math. Sin. Engl. Ser. 25(9), 1437–1442 (2009). doi:10.1007/s10114-009-6292-y
Andrews, G.: The Theory of Partitions. The Encyclopedia of Mathematics and Its Applications Series. Addison-Wesley, New York (1976), 300 pp. Reissued, Cambridge University Press, New York (1998)
Stockhofe, D.: Bijektive Abbildungen auf der Menge der Partitionen einer Naturlichen Zahl. Bayreuth. Math. Schr. 10, 1–59 (1982)
Keith, W.: Ranks of Partitions and Durfee Symbols. Ph.D. Thesis, Pennsylvania State University (June 2007). URL: http://etda.libraries.psu.edu/theses/approved/WorldWideIndex/ETD-2026/index.html
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Keith, W.J. A bijection for partitions with initial repetitions. Ramanujan J 27, 163–167 (2012). https://doi.org/10.1007/s11139-011-9298-x