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In a recent author's work the cyclic behavior of maxima in a hierarchicalsummation scheme was discovered. In the present note we show how the samephenomenon appears in the scheme of conventional summation: the distribution ofmaximum of $2^n$ independent copies of a sum of $n$ i.i.d. random variablesapproaches, as $n$ grows, some helix in the space of distributions.

Cyclic behavior of maxima for sums of independent variables