Erdős problem 36 · problems.science

This example calculates the value of $M 1$ . The set is $\{1, 2\}$ , so the only partition is $A = \{1\}, B = \{2\}$ (or vice versa). The possible differences are $1 - 2 = -1$ and $2 - 1 = 1$ . The Overlap for $k=-1$ is 1 (if $A=\{1\}, B=\{2\}$ ) and for $k=1$ also 1 (if $A=\{2\}, B=\{1\}$ ). The MaxOverlap is $1$ , since the Overlap is $0$ for other $k$ . Thus, $M 1 = 1$ .

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36.lean

Retained formal statement9 of 18

For $n = 2$ , the set is $\{1, 2, 3, 4\}$ . The balanced partition $A = \{1, 4\}, B = \{2, 3\}$ has all four pairwise differences ( $\pm 1, \pm 2$ ) distinct, so MaxOverlap = 1. Any balanced partition has both pieces nonempty, so MaxOverlap \geq 1.

FormalConjectures/ErdosProblems/36.leanErdos36.M_two1 lineExact file

1Erdos36.M 2 = 1

TestStatement only, no proof

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