Andrews, GeorgeGeorgeAndrewsChan, Song HengSong HengChanKim, ByungchanByungchanKimOsburn, RobertRobertOsburn2016-09-162017-02-022016 Sprin2016-06Annals of Combinatoricshttp://hdl.handle.net/10197/7951In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting.enThe final publication is available at Springer via http://dx.doi.org/10.1007/s00026-016-0306-0.OverpartitionsRanksCranksPositive momentsPositivityJournal Article20219320710.1007/s00026-016-0306-02016-08-10https://creativecommons.org/licenses/by-nc-nd/3.0/ie/