Counting designs

By Peter Keevash. 2015

52 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/3bde2628087001ab1ad5313e84e8bd93c72b93d4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

The Existence of Designs via Iterative Absorption: Hypergraph 𝐹-designs for Arbitrary 𝐹 (2016, background): “K (r) n (see [23, 24] for the clique case).”
The existence of designs via iterative absorption (2016, result): “We also note that, in a similar way as discussed in [20, 21], the results of this paper can be combined with ‘counting versions’ of the Rödl nibble (or corresponding random greedy processes) to obtain lower bounds on the number of designs with given parameters.”
Almost all Steiner triple systems have perfect matchings (2016, background): “meansthereisaconstantc>0 suchthatfcjgj, f= ( g) meansthatf= O(g) andf= (g), f= o(g) meansthatf=g!0 asn!1. Tosaythata.a.s. f= o(g) meansthatforany ">0,a.a.s. f=g<". Also,following[27],thenotationf= 1 "means1 "f1 + ". We also use standard graph theory notation: V(G) a”