8 papers · 1 filter
The Brown-Erdős-Sós Conjecture for hypergraphs of large uniformity
Peter Keevash, Jason Long
We prove the well-known Brown-Erdős-Sós Conjecture for hypergraphs of large uniformity in the following form: any dense linear -graph has edges spanning at most $(r-2)k+…
A universal exponent for homeomorphs
Peter Keevash, Jason Long, Bhargav Narayanan +1
We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex : any -vertex two-dimensional complex with at least $C_S n^{3-1/5}…
The extremal number of Venn diagrams
Peter Keevash, Imre Leader, Jason Long +1
We show that there exists an absolute constant such that any family of size at least has dual VC-dimension at least 3. Equivalently, eve…
The performance guarantee of randomized perfect voting trees
Jason Long, Adam Zsolt Wagner
In this note we study randomized voting trees, previously introduced by Fisher, Procaccia and Samorodnitsky. They speculate that a non-trivial performance guarantee may be achievab…
Partial associativity and rough approximate groups
W. T. Gowers, Jason Long
Suppose that a binary operation on a finite set is injective in each variable separately and also associative. It is easy to prove that must be a group. In…
A note on the Brown--Erdős--Sós conjecture in groups
Jason Long
We show that a dense subset of a sufficiently large group multiplication table contains either a large part of the addition table of the integers modulo some , or the entire mul…