Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups

Binzhou Xia; Cheryl E. Praeger; Jing Jian Li; Junyan Chen; Lei Chen; Michael Giudici

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arxiv 2111.06579 v2 pith:RN6YOGGU submitted 2021-11-12 math.CO

Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

Junyan Chen , Lei Chen , Michael Giudici , Jing Jian Li , Cheryl E. Praeger , Binzhou Xia This is my paper

classification math.CO

keywords arc-transitivegroupalternatingbounddigraphssymmetricuppervertex-primitive

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Determining an upper bound on $s$ for finite vertex-primitive $s$-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 $s$ is attained for some digraph admitting an almost simple $s$-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that $s\leqslant 2$ in the case where the group is an alternating or symmetric group.

Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups

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