Erdős Problem #103
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The sets of \(n\) points in \(\mathbb{R}^2\) whose pairwise distances are all at least \(1\).
`A` is a *minimiser* for `n` if it is a separated set of `n` points whose diameter is at most the diameter of every separated set of `n` points (compare `Erdos99.erdos_99`).
Two finite sets of points are *congruent* if an isometry of the plane maps one onto the other.
Let \(h(n)\) count the number of incongruent sets of \(n\) points in \(\mathbb{R}^2\) which minimise the diameter subject to the constraint that \(d(x,y)\geq 1\) for all points \(x\neq y\). Is it true that \(h(n)\to \infty\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/103.Attempts
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