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Journal of the London Mathematical Society 1992 s2-45(2):222-231; doi:10.1112/jlms/s2-45.2.222
© 1992 by London Mathematical Society
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© Oxford University Press

Relations Between the Rank and the Crank Modulo 9

Richard Lewis

School of Mathematical and Physical Sciences, University of Sussex Brighton BN1 9QH

In [10] various conjectural identities between the ranks and the cranks of partitions modulo 8, 9 and 12 were proposed. These conjectures have now all been proved [14, 15, 11], with three exceptions. Here, we prove these three exceptions. Methods similar to those used here may be used to establish all the theorems and conjectures of [10].


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