Sean Eberhard

activity

20162021

most citedThe trivial lower bound for the girth of

S_{n}

4 citations · 11 across the 4 of their papers we have counts for

collaborators

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5 papers · 1 filter

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.GR2021★ 3 cited

Sharply transitive sets in $PGL_{2} (K)$

Sean Eberhard

Here is a simplified proof that every sharply transitive subset of $PGL_{2} (K)$ is a coset of a subgroup.

math.GR2019

Association schemes for diagonal groups

Peter J. Cameron, Sean Eberhard

For any finite group $G$ , and any positive integer $n$ , we construct an association scheme which admits the diagonal group $D_{n} (G)$ as a group of automorphisms. The rank of the ass…

math.GR2018

Random generation under the Ewens distribution

Sean Eberhard

The Ewens sampling formula with parameter $α$ is the distribution on $S_{n}$ which gives each $π \in S_{n}$ weight proportional to $α^{C (π)}$ , where $C (π)$ is the number of cycles of $π…

math.GR2017★ 4 cited

The trivial lower bound for the girth of $S_{n}$

Sean Eberhard

Consider the Cayley graph of $S_{n}$ generated by a random pair of elements $x, y$ . Conjecturally, the girth of this graph is $Ω (n lo g n)$ with probability tending to $1$ as $n\to\in…

Probability of generation by random permutations of given cycle type

Sharply transitive sets in PGL2​(K)

Association schemes for diagonal groups

Random generation under the Ewens distribution

The trivial lower bound for the girth of Sn​

Sharply transitive sets in $PGL_{2} (K)$

The trivial lower bound for the girth of $S_{n}$