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Erdős problem 34

For any permutation π∈Sn\pi\in S_n of {1,…,n}\{1,\ldots,n\} let S(π)S(\pi) count the number of distinct consecutive sums, that is, sums of the shape ∑u≤i≤vπ(i)\sum_{u\leq i\leq v}\pi(i). Is it true that S(π)=o(n2) S(\pi) = o(n^2) for all π∈Sn\pi\in S_n?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/34.lean

Formal Conjectures

FormalConjectures/ErdosProblems/34.leanErdos34.erdos_341 lineExact file
False ↔ ∀ (c : ℝ), 0 < c → ∃ N, ∀ n ≥ N, ∀ (p : Equiv.Perm (Fin n)), ↑(Erdos34.consecutiveSums n p).card < c * ↑n ^ 2
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:34
  • PLBY Lean proofsErdosProblems.Erdos34

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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