Let f_d(n) be minimal such that, in any set of n points in R^d, there exist at most f_d(n) pairs of points which distance 1 apart. Estimate f_d(n).

Erdős Problem #1085 — Let $f_d(n)$ be minimal such that, in any set of $n$ points in $\mathbb{R}^d$ , there exist at most $f_d(n)$ pairs of points which distance $1$ apart.

About 51 years old · traced to 1975

Let $f_d(n)$ be minimal such that, in any set of $n$ points in $\mathbb{R}^d$ , there exist at most $f_d(n)$ pairs of points which distance $1$ apart. Estimate $f_d(n)$ .

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

distances geometry

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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