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Random recursive hypergraphs (RRHs) grow by adding, at each step, a vertex and an edge formed by joining the new vertex to a randomly chosen existing edge. The model is parameter-free, and several characteristics of emerging hypergraphs admit neat expressions via harmonic numbers, Bernoulli numbers, Eulerian numbers, and Stirling numbers of the first kind. Natural deformations of RRHs give rise to fascinating models of growing random hypergraphs.
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P. L. Krapivsky (2023) studied this question.
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