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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.
Hopkins et al. (2020) studied this question.