Erdős problem 1026 · problems.science

For a sequence of $n$ distinct reals, determine the largest constant $c$ such that some monotonic subsequence always has sum exceeding $(c-o(1))\cdot(1/\sqrt{n})$ times the total sum. Resolved as $c = 1$ .

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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1026.lean

Retained formal statement4 of 6

Hanani [Ha57] showed that every sequence is the disjoint union of at most $(\sqrt{2}+o(1))\sqrt{n}$ many monotonic subsequences, whence $c\geq 1/\sqrt{2}$ .

FormalConjectures/ErdosProblems/1026.leanErdos1026.erdos_1026.variants.lower_bound1 lineExact file

11 / √2 ∈ Erdos1026.admissibleConstants

SolvedStatement only, no proof

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