Shasha Zheng

collaborators

5 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.CO2022

Asymptotic enumeration of graphical regular representations

Binzhou Xia, Shasha Zheng

We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have ful…

math.GR2022

Cubic graphical regular representations of some classical simple groups

Binzhou Xia, Shasha Zheng, Sanming Zhou

A graphical regular representation (GRR) of a group $G$ is a Cayley graph of $G$ whose full automorphism group is equal to the right regular permutation representation of $G$ . In t…

math.GR2022

Cubic Graphical Regular Representations of $PSU_{3} (q)$

Jing Jian Li, Binzhou Xia, Xiao Qian Zhang +1

A graphical regular representation (GRR) of a group $G$ is a Cayley graph of $G$ whose full automorphism group is equal to the right regular permutation representation of $G$ . Towa…

Asymptotic enumeration of minimally transitive permutation groups

Asymptotic stability of Cayley graphs on abelian groups

Asymptotic enumeration of graphical regular representations

Cubic graphical regular representations of some classical simple groups

Cubic Graphical Regular Representations of PSU3​(q)

Cubic Graphical Regular Representations of $PSU_{3} (q)$