Geodesic
Counting designs
Journal of the European Mathematical Society, Tome 20 (2018) no. 4, pp. 903-927

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We give estimates on the number of combinatorial designs, which prove (and generalise) a conjecture of Wilson from 1974 on the number of Steiner Triple Systems. This paper also serves as an expository treatment of our recently developed method of Randomised Algebraic Construction: we give a simpler proof of a special case of our result on clique decompositions of hypergraphs, namely triangle decompositions of quasirandom graphs.
DOI : 10.4171/jems/779
Classification : 05-XX
Keywords: Hypergraph Decomposition, Design Theory 
Peter Keevash. Counting designs. Journal of the European Mathematical Society, Tome 20 (2018) no. 4, pp. 903-927. doi: 10.4171/jems/779
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