Abstract
Let d ∈ d∈ℕ, d≥2 ≥ 2. We prove that for almost all partitions of an integer the parts are well distributed in residue classes mod d. The limitations of the uniformity of this distribution are also studied.
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References
J. Dixmier and J.-L. Nicolas, “Partitions without small parts,” Number Theory 1 (Budapest, 1987), Colloq. Math. Soc. J. Bolyai 51 (North-Holland, Amsterdam, 1990), 9–33.
P. Erdős and J. Lehner, “The distribution of the number of summands in the partitions of a positive integer,” Duke Math. Journal 8 (1941), 335–345.
P. Erdős, J.-L. Nicolas, and A. Sárközy, “On the number of partitions of n without a given subsum (I),” Discrete Math. 75 (1989), 155–166.
P. Erdős and M. Szalay, “Note to Turán paper's on the statistical theory of groups and partitions,” in Collected Papers of Paul Tur´ an, Akadémiai Kiadó, Budapest, 3 (1990), 2583–2603.
G.H. Hardy and S. Ramanujan, “Asymptotic formulae in combinatory analysis,” Proceedings of the London Math. Soc. 17 (1918), 465–490.
G. Meinardus, “Asymptotische Aussagen über Partitionen,” Math. Zeitschr. Bd. 59 (1954), 388–398.
M. Szalay, “Statistical properties of partitions,” Turán Memorial week, Oct. 2–6, 2000.
M. Szalay and P. Turán, “On some problems of a statistical theory of partitions with application to character of the symmetric group III,” Acta Math. Acad. Sci. Hungar. 32 (1978), 129–155.
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Dartyge, C., Sárközy, A. Arithmetic Properties of Summands of Partitions. The Ramanujan Journal 8, 199–215 (2004). https://doi.org/10.1023/B:RAMA.0000040481.02788.ae
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DOI: https://doi.org/10.1023/B:RAMA.0000040481.02788.ae