25 citations · 88 across the 11 of their papers we have counts for
8 papers · 1 filter
Transversals in quasirandom latin squares
Sean Eberhard, Freddie Manners, Rudi Mrazović
A transversal in an latin square is a collection of entries not repeating any row, column, or symbol. Kwan showed that almost every latin square has $…
The apparent structure of dense Sidon sets
Sean Eberhard, Freddie Manners
The correspondence between perfect difference sets and transitive projective planes is well-known. We observe that all known dense (i.e., close to square-root size) Sidon subsets o…
An asymptotic for the Hall--Paige conjecture
Sean Eberhard, Freddie Manners, Rudi Mrazović
Hall and Paige conjectured in 1955 that a finite group has a complete mapping if and only if its Sylow -subgroups are trivial or noncyclic. This conjecture was proved in 200…
A proof of Tomescu's graph coloring conjecture
Jacob Fox, Xiaoyu He, Freddie Manners
In 1971, Tomescu conjectured that every connected graph on vertices with chromatic number has at most proper -colorings. Recently, Knox and Moha…
Finding a low-dimensional piece of a set of integers
Freddie Manners
We show that a finite set of integers with contains a large piece with Freĭman dimension , where large means $…
Additive triples of bijections, or the toroidal semiqueens problem
Sean Eberhard, Freddie Manners, Rudi Mrazović
We prove an asymptotic for the number of additive triples of bijections , that is, the number of pairs of bijections $π_1,π_2\colon \{1,\dot…
A solution to the Pyjama Problem
Freddie Manners
The "pyjama stripe" is the subset of consisting of a vertical strip of width around every integer -coordinate. The "pyjama problem" asks whether f…
Sets of integers with no large sum-free subset
Sean Eberhard, Ben Green, Freddie Manners
Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n…