On a phenomenon of Turán concerning the summands of partitions

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 1/ 2 − ε with ε > 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.
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Cécile Dartyge, Mihály Szalay. On a phenomenon of Turán concerning the summands of partitions. Acta Mathematica Hungarica, Springer Verlag, 2016, 149 (2), pp.375-395. ⟨10.1007/s10474-016-0623-0⟩. ⟨hal-01280845⟩

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