3-Uniform Friendship Hypergraphs

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Today we discuss On a question of Sós about 3-uniform friendship hypergraphs by Hartke and Vandenbussche. These authors presented several new examples of friendship hypergraphs exhibiting a property that was not known to be possible. Their method applies careful use of integer programming as a black box. First, a careful construction of an integer linear program discovered some examples (and non-existence of examples) for small orders. Then, by making some symmetry assumptions, they constructed some larger integer programs that found larger examples, hinting towards an infinite family. The existence of larger examples remains open, although Lia, van Reesa, Seoa, and Singhi recently proved some structure theorems that apply to the examples found by Hartke and Vandenbussche.
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