Turning the Partition Crank

Brian Hopkins, James A. Sellers

Research output: Contribution to journalComment/debatepeer-review

9 Scopus citations


After reviewing the history of the crank of an integer partition, involving work of Freeman Dyson from 1944 and Frank Garvan and George Andrews in 1988, we connect this concept with more recent work of Andrews based on the smallest missing part of a partition. This alternative view of partitions having certain crank values allows us to strengthen a recent result of Yuefei Shen with a greatly simplified and more insightful proof.

Original languageEnglish (US)
Pages (from-to)654-657
Number of pages4
JournalAmerican Mathematical Monthly
Issue number7
StatePublished - Aug 8 2020


  • MSC: Primary 11P84
  • Secondary 05A17


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