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erdős #34

← #33 · #35 → (packet.json; erdosproblems.com)

For any permutation $π \in S_{n}$ of ${1, \dots, n}$ let $S (π)$ count the number of distinct consecutive sums, that is, sums of the shape $\sum_{u \leq i \leq v} π (i)$ . Is it true that $S (π) = o (n^{2})$ for all $π \in S_{n}$ ?

Worked, still open.

number theory · solved · 0 attempts

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A234813 — Number of distinct integers of the form i+(i+1)+(i+2)+...+j, for 1 <= i <= j <= n.1,3,5,9,12,16,21,27,33,40,47,55,63,70,77,89,101,110,123,134,146,159,171,186,200,214,229,245,260,275,293,312,329,349,369,A389241 — Maximum number of distinct consecutive sums of a permutation of [n].0,1,3,6,9,13,19,25,32,39,47,56,66,77,89,100 A390187 — Minimum number of distinct consecutive sums of a permutation of [n].0,1,3,5,7,10,13,17,20,25,30,33,39,44,50,56,63,70,77

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solved

finding.noted · reviewer:will-blair · 1 day

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