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Multi-way expanders and imprimitive group actions on graphs
For n at least 2, the concept of n-way expanders was defined by various
researchers. Bigger n gives a weaker notion in general, and 2-way expanders
coincide with expanders in usual sense. Koji Fujiwara asked whether these
concepts are equivalent to that of ordinary expanders for all n for a sequence
of Cayley graphs. In this paper, we answer his question in the affirmative.
Furthermore, we obtain universal inequalities on multi-way isoperimetric
constants on any finite connected vertex-transitive graph, and show that gaps
between these constants imply the imprimitivity of the group action on the
graph.Comment: Accepted in Int. Math. Res. Notices. 18 pages, rearrange all of the
arguments in the proof of Main Theorem (Theorem A) in a much accessible way
(v4); 14 pages, appendix splitted into a forthcoming preprint (v3); 17 pages,
appendix on noncommutative L_p spaces added (v2); 12 pages, no figure
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