Erdős Problem #1026

The problem

Let $x_1,\ldots,x_n$ be a sequence of distinct real numbers. Determine

$$\max\left(\sum x_{i_r}\right),$$

where the maximum is taken over all monotonic subsequences.

Statement quoted from erdosproblems.com/1026, maintained by Thomas Bloom. Original source: [Er71,p.107]. Current status there: solved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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