On the rank and the crank modulo and

Authors:
Richard Lewis and Nicolas Santa-Gadea

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove some identities, conjectured by Lewis, for the rank and crank of partitions concerning the modulo and . These identities are similar to Dyson's identities for the rank modulo and 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1136545-0

Keywords:
Partitions,
rank,
crank,
mock theta functions

Article copyright:
© Copyright 1994
American Mathematical Society