Sean Eberhard

activity

20122023

most citedCommuting probabilities of finite groups

34 citations · 245 across the 36 of their papers we have counts for

collaborators

Showing 2015Show all

5 papers · 1 filter

math.GR2015★ 3 cited

Product mixing in the alternating group

Sean Eberhard

We prove the following one-sided product-mixing theorem for the alternating group: Given subsets $X, Y, Z \subset A_{n}$ of densities $α, β, γ$ satisfying $\min(αβ,αγ,βγ)\gg n^{-1}(\log…

math.GR2015★ 2 cited

A note on nonabelian Freiman-Ruzsa

Sean Eberhard

Recently Breuillard and Tointon showed that one reasonable formulation of the polynomial Freiman-Ruzsa conjecture fails for nonabelian groups. We improve and simplify their constru…

math.CO2015★ 25 cited

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 ${1, \dots, n} \to Z / n Z$ , that is, the number of pairs of bijections $π_1,π_2\colon \{1,\dot…

math.GR2015★ 16 cited

Invariable generation of the symmetric group

Sean Eberhard, Kevin Ford, Ben Green

We say that permutations $π_{1}, \dots, π_{r} \in S_{n}$ invariably generate $S_{n}$ if, no matter how one chooses conjugates $π_{1}^{'}, \dots, π_{r}^{'}$ of these permutations, $π…

math.CO2015★ 18 cited

Permutations fixing a k-set

Sean Eberhard, Kevin Ford, Ben Green

Let $i (n, k)$ be the proportion of permutations $π \in S_{n}$ having an invariant set of size $k$ . In this note we adapt arguments of the second author to prove that $i(n,k) \…