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On the rank and the crank modulo $ 4$


Author: Richard Lewis
Journal: Proc. Amer. Math. Soc. 112 (1991), 925-933
MSC: Primary 11P83
DOI: https://doi.org/10.1090/S0002-9939-1991-1057957-2
MathSciNet review: 1057957
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Abstract: Let $ N(r,m,n)$ (respectively, $ M(r,m,n)$) denote the number of partitions of $ n$ whose ranks (respectively, cranks) are congruent to $ r$ modulo $ n$. It is shown that $ N(0,4,2n + 1) = M(1,4,2n + 1)$ and $ N(2,4,2n) = M(1,4,2n)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1057957-2
Keywords: Partition, rank, crank
Article copyright: © Copyright 1991 American Mathematical Society

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