Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Problem 734

Statement. Find, for all large $n$ , a non-trivial pairwise balanced block design $A_1,\ldots,A_m\subseteq \{1,\ldots,n\}$ such that, for all $t$ , there are $O(n^{1/2})$ many $i$ such that $\lvert A_i\rvert=t$ .

Status. Open.

Source. erdosproblems.com/734, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #734, https://www.erdosproblems.com/734.

References.

[Er81] Erdős, P., On the combinatorial problems which I would most like to see solved. Combinatorica (1981), 25-42.
[dBEr48] de Bruijn, N. G. and Erdős, P., On a combinatorial problem. Nederl. Akad. Wetensch., Proc. (1948), 1277-1279 = Indagationes Math. 10, 421-423.

Formalization. Statement in formal-conjectures.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

Linked from (4)

Set Systems, Designs and Hypergraphs set_systems/bruijn_1948_combinatorial_problem Theorem 1 (p. 421): more than one block covering every pair of n points exactly once means at least n blocks set_systems/erdos_1981_combinatorial_problems_which_i_would_most

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