Acta Mathematica Hungarica

, Volume 149, Issue 2, pp 375–395 | Cite as

On a phenomenon of Turán concerning the summands of partitions

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Abstract

Turán [12] proved that for almost all pairs of partitions of an integer, the proportion of common parts is very high, that is greater than \({\frac{1}{2} - \varepsilon}\) with \({\varepsilon > 0}\) arbitrarily small. In this paper we prove that this surprising phenomenon persists when we look only at the summands in a fixed arithmetic progression.

Mathematics Subject Classification

primary 11P82 secondary 05A17 11P83 

Key words and phrases

pair of partitions common part in residue classes 
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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Institut Élie CartanUniversité de LorraineVandœuvre CedexFrance
  2. 2.Department of Algebra and Number TheoryEötvös Loránd UniversityBudapestHungary

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