Binzhou Xia

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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.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…