The existence of designs
Combinatorics
2024-11-28 v4
Abstract
We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that satisfy a certain pseudorandomness condition. As a further generalisation, we obtain the same conclusion only assuming an extendability property and the existence of a robust fractional clique decomposition.
Cite
@article{arxiv.1401.3665,
title = {The existence of designs},
author = {Peter Keevash},
journal= {arXiv preprint arXiv:1401.3665},
year = {2024}
}
Comments
Version 4 (the decennial edition) incorporates referee comments, additional exposition and a brief review of subsequent work