New identities for 7-cores with prescribed BG-rank

@article{Berkovich2008NewIF,
  title={New identities for 7-cores with prescribed BG-rank},
  author={Alexander Berkovich and Hamza Yesilyurt},
  journal={Discrete Mathematics},
  year={2008},
  volume={308},
  pages={5246-5259}
}
Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [1]. In [2], Berkovich and Garvan found theta series representations for the t-core generating functions P n≥0 at,j(n)q , where at,j(n) denotes the number of t-cores of n with BG-rank = j. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme values of BG-rank. In this paper we discuss representations of this type for all 7-cores with prescribed BG… CONTINUE READING

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