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Nicolaas Govert de Bruijn worked on combinatorics and mathematical structures. With Paul Erdős, he proved a finite incidence theorem in their 1948 paper: a nontrivial system in which each pair of points lies on exactly one line has at least as many lines as points.[ref]
The equality cases are highly organized: a near-pencil or a finite projective plane. This shows how a local pair-incidence rule controls both a global counting inequality and the structure of extremal examples.[ref]