On the rank and the crank modulo $4$ and $8$
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- by Richard Lewis and Nicolas Santa-Gadea
- Trans. Amer. Math. Soc. 341 (1994), 449-465
- DOI: https://doi.org/10.1090/S0002-9947-1994-1136545-0
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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.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 341 (1994), 449-465
- MSC: Primary 11P83; Secondary 05A17
- DOI: https://doi.org/10.1090/S0002-9947-1994-1136545-0
- MathSciNet review: 1136545