Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups
Combinatorics
2024-02-23 v2
Abstract
Determining an upper bound on for finite vertex-primitive -arc-transitive digraphs has received considerable attention dating back to a question of Praeger in 1990. It was shown by Giudici and Xia that the smallest upper bound on is attained for some digraph admitting an almost simple -arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that in the case where the group is an alternating or symmetric group.
Cite
@article{arxiv.2111.06579,
title = {Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups},
author = {Junyan Chen and Lei Chen and Michael Giudici and Jing Jian Li and Cheryl E. Praeger and Binzhou Xia},
journal= {arXiv preprint arXiv:2111.06579},
year = {2024}
}