6 papers
An infinite family of counterexamples to the Polycirculant Conjecture
Saul D. Freedman, Melissa Lee
We disprove the Polycirculant Conjecture, which states that every transitive 2-closed permutation group is non-elusive, i.e. contains a derangement of prime order. In fact, we prov…
Automorphisms of Kimura Hadamard Matrices
Santiago Barrera Acevedo, Melissa Lee
We investigate the structure of the automorphism groups of Kimura Hadamard matrices (KHMs) constructed from dihedral groups. We identify several different types of automorphisms, a…
Prime simplicial complexes of finite groups
Melissa Lee, Kamilla Rekvényi
The prime simplicial complex of a finite group is composed of all sets of primes where has an element of order the product of primes in , with the subsets par…
The Saxl hypergraph of a permutation group
Melissa Lee, Anthony Pisani
Given a permutation group , a subset of is said to be a base if its pointwise stabiliser in is trivial, and the base size is the minimum s…
On the generalised Saxl graphs of permutation groups
Saul D. Freedman, Hong Yi Huang, Melissa Lee +1
A base for a finite permutation group is a subset of with trivial pointwise stabiliser in , and the base size of is the smallest size of a base f…
On the diameter of intersection graphs of finite groups
Melissa Lee, Kamilla Rekvényi
The intersection graph of a finite group is a simple graph with vertices the non-trivial proper subgroups of , and an edge between two vertices if their corresponding…