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Aug 30, 2012 at 14:52 answer added Joel Adler timeline score: 2
Aug 30, 2012 at 11:50 comment added Patricia Hersh Todd Trimble has pointed out to me that this does not give a counterexample. You can find a picture of this example at en.wikipedia.org/wiki/Noncrossing_partition. Good luck with your work!
Aug 30, 2012 at 5:28 vote accept Colin Reid
Aug 30, 2012 at 1:28 answer added Todd Trimble timeline score: 6
Aug 30, 2012 at 0:28 answer added Tom Leinster timeline score: 2
Aug 30, 2012 at 0:20 comment added Patricia Hersh I haven't thought about this carefully, but are you sure that the noncrossing partition lattice of rank 3 doesn't also satisfy all your conditions?
Aug 30, 2012 at 0:00 history asked Colin Reid CC BY-SA 3.0