Binzhou Xia

collaborators

4 papers

math.GR2026

Asymptotic enumeration of minimally transitive permutation groups

Binzhou Xia, Shasha Zheng

We prove that Pyber's upper bound $2^{O (n l o g (n))}$ for the number of minimally transitive subgroups of $S_{n}$ is best possible along the powers of every fixed prime, even when the…

math.CO2026

Asymptotic stability of Cayley graphs on abelian groups

Binzhou Xia, Zhishuo Zhang, Shasha Zheng

For a finite group $G$ , we say that a Cayley graph $Γ$ on $G$ is a most rigid representation (MRR) of $G$ if its full automorphism group has the smallest possible order among all C…

math.GR2025

On automorphism groups of half-arc-transitive tetravalent graphs

Yuandong Li, Binzhou Xia, Jin-Xin Zhou

We characterize connected tetravalent graphs $Γ$ which admit groups $M < H$ of automorphisms such that $Γ$ is $M$ -half-arc-transitive and $H$ -arc-transitive. Examples for each case a…

math.CO2025

The existence of unexpected automorphisms in direct product graphs

Xiaomeng Wang, Yan-Li Qin, Binzhou Xia

A pair of graphs $(Γ, Σ)$ is called unstable if their direct product $Γ \times Σ$ admits automorphisms not from $Aut (Γ) \times Aut (Σ)$ , and such automorphisms are said…