English

Counting designs

Combinatorics 2015-04-14 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1504.02909,
  title  = {Counting designs},
  author = {Peter Keevash},
  journal= {arXiv preprint arXiv:1504.02909},
  year   = {2015}
}

Comments

24 pages, 2 figures

R2 v1 2026-06-22T09:14:35.746Z