The Ramanujan Journal

, Volume 23, Issue 1, pp 195–213

Cluster parity indices of partitions


DOI: 10.1007/s11139-009-9209-6

Cite this article as:
Kurşungöz, K. Ramanujan J (2010) 23: 195. doi:10.1007/s11139-009-9209-6


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.


Integer partition Cluster parity index 

Mathematics Subject Classification (2000)

05A17 05A15 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity ParkUSA

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