Sean Eberhard

activity

20122023

most citedCommuting probabilities of finite groups

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

collaborators

36 papers

math.GR2023

Diameter of classical groups generated by transvections

Sean Eberhard

Let $G$ be a finite classical group generated by transvections, i.e., one of $SL_{n} (q)$ , $SU_{n} (q)$ , $Sp_{2 n} (q)$ , or $\operatorname{O}^\…

math.GR2023★ 1 cited

Dixon's asymptotic without CFSG

Sean Eberhard

Without using the classification of finite simple groups, we show that the probability that two random elements of $S_{n}$ generate a primitive group smaller than $A_{n}$ is at most $\…

math.GR2023★ 3 cited

Conjugacy classes of derangements in finite groups of Lie type

Sean Eberhard, Daniele Garzoni

Let $G$ be a finite almost simple group of Lie type acting faithfully and primitively on a set $Ω$ . We prove an analogue of the Boston--Shalev conjecture for conjugacy classes: the…

math.CO2022★ 4 cited

Transversals in quasirandom latin squares

Sean Eberhard, Freddie Manners, Rudi Mrazović

A transversal in an $n \times n$ latin square is a collection of $n$ entries not repeating any row, column, or symbol. Kwan showed that almost every $n \times n$ latin square has $…

math.GR2022

Probability of generation by random permutations of given cycle type

Sean Eberhard, Daniele Garzoni

Suppose $π$ and $π^{'}$ are two random elements of $S_{n}$ with constrained cycle types such that $π$ has $x n^{1/2}$ fixed points and $y n /2$ two-cycles, and likewise $π^{'}$ has $x' n^{1/…

math.CO2022

Fusions of tensor powers of Johnson schemes

Sean Eberhard, Mikhail Muzychuk

This paper is a follow-up to (arXiv:2203.03687), in which the first author studied primitive association schemes lying between a tensor power $T_{m}^{d}$ of the trivial assoc…