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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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