Turning the Partition Crank

Brian Hopkins; James A. Sellers

doi:10.1080/00029890.2020.1755584

Turning the Partition Crank

Brian Hopkins, James A. Sellers

Mathematics & Statistics

Research output: Contribution to journal › Comment/debate › peer-review

10 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	654-657
Number of pages	4
Journal	American Mathematical Monthly
Volume	127
Issue number	7
DOIs	https://doi.org/10.1080/00029890.2020.1755584
State	Published - Aug 8 2020

Keywords

MSC: Primary 11P84
Secondary 05A17

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10.1080/00029890.2020.1755584

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Turning the Partition Crank

Abstract

Keywords

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