Counting designs

  • Peter Keevash

    University of Oxford, UK


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.

Cite this article

Peter Keevash, Counting designs. J. Eur. Math. Soc. 20 (2018), no. 4, pp. 903–927

DOI 10.4171/JEMS/779