Melissa Lee

collaborators

5 papers

math.GR2026

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…

math.CO2026

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…

math.GR2026

On the generalised Saxl graphs of permutation groups

Saul D. Freedman, Hong Yi Huang, Melissa Lee +1

A base for a finite permutation group $G \leq Sym (I^c ◯)$ is a subset of $I^c ◯$ with trivial pointwise stabiliser in $G$ , and the base size of $G$ is the smallest size of a base…

math.GR2025

Prime simplicial complexes of finite groups

The prime simplicial complex $I^(G)$ of a finite group $G$ is composed of all sets of primes $S$ where $G$ has an element of order the product of primes in $S$ , with the subsets pa…

math.GR2025

The Saxl hypergraph of a permutation group

Melissa Lee, Anthony Pisani

Given a permutation group $G \leq Sym (I^c ◯)$ , a subset $B$ of $I^c ◯$ is said to be a base if its pointwise stabiliser in $G$ is trivial, and the base size $b (G)$ is the minimum…