## 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