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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the rank and the crank modulo $ 4$ and $ 8$

Authors: Richard Lewis and Nicolas Santa-Gadea
Journal: Trans. Amer. Math. Soc. 341 (1994), 449-465
MSC: Primary 11P83; Secondary 05A17
MathSciNet review: 1136545
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Abstract: In this paper we prove some identities, conjectured by Lewis, for the rank and crank of partitions concerning the modulo $ 4$ and $ 8$. These identities are similar to Dyson's identities for the rank modulo $ 5$ and $ 7$ which give a combinatorial interpretation to Ramanujan's partition congruences. For this, we use multisection of series and some of the results that Watson established for the third order mock theta functions.

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Keywords: Partitions, rank, crank, mock theta functions
Article copyright: © Copyright 1994 American Mathematical Society

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