Cluster parity indices of partitions
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Andrews recently made an extensive study of parity in partition identities. One of the open questions he listed was to describe the partitions enumerated by a series. The series resembled the series side of the Andrews–Gordon Identities with an extra parameter, and it seemed to have properties related to the parity indices, which are defined by Andrews. We define cluster parity indices, and settle the problem.
KeywordsInteger partition Cluster parity index
Mathematics Subject Classification (2000)05A17 05A15
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