Freddie Manners

activity

20132026

most citedAdditive triples of bijections, or the toroidal semiqueens problem

25 citations · 88 across the 11 of their papers we have counts for

collaborators

Showing 2017Show all

3 papers · 1 filter

math.CO2017

A proof of Tomescu's graph coloring conjecture

Jacob Fox, Xiaoyu He, Freddie Manners

In 1971, Tomescu conjectured that every connected graph $G$ on $n$ vertices with chromatic number $k \geq 4$ has at most $k! (k - 1)^{n - k}$ proper $k$ -colorings. Recently, Knox and Moha…

math.NT2017

Formulations of the PFR Conjecture over $Z$

Freddie Manners

The polynomial Fre\uıman--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally $R^{d}$ or $Z^{d}$ )…

math.NT2017★ 3 cited

Good Bounds in Certain Systems of True Complexity One

Freddie Manners

Let $Φ = (ϕ_{1}, \dots, ϕ_{6})$ be a system of $6$ linear forms in $3$ variables, i.e. $ϕ_{i} : Z^{3} \to Z$ for each $i$ . Suppose also that $Φ$ has Cauchy--Schwarz com…

A proof of Tomescu's graph coloring conjecture

Formulations of the PFR Conjecture over Z

Good Bounds in Certain Systems of True Complexity One

Formulations of the PFR Conjecture over $Z$