11798 8 archive 1 disk0/00/01/17/98 2008-09-29 23:19:32 2008-09-29 23:19:32 2008-09-29 23:19:32 article show 0 Bonderson Parsa Bonderson-P Slingerland J. K. Slingerland-J-K pub cls public ground states; Landau levels; quantum Hall effect ©2008 The American Physical Society. (Received 24 July 2008; revised 19 August 2008; published 26 September 2008) We thank Jim Eisenstein, Adrian Feiguin, Woowon Kang, Chetan Nayak, Wei Pan, Ed Rezayi, Kirill Shtengel, and Steve Simon for illuminating discussions. We also acknowledge the hospitality of the IQI, Microsoft Station Q, and the Aspen Center for Physics. This work was supported in part by the NSF under Grant No. PHY-0456720 and the ARO under Contract No. W911NF-05-1-0294. We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. 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