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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Partition theorems related to some identities of Rogers and Watson
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by Willard G. Connor PDF
Trans. Amer. Math. Soc. 214 (1975), 95-111 Request permission

Abstract:

This paper proves two general partition theorems and several special cases of each with both of the general theorems based on four q-series identities originally due to L. J. Rogers and G. N. Watson. One of the most interesting special cases proves that the number of partitions of an integer n into parts where even parts may not be repeated, and where odd parts occur only if an adjacent even part occurs is equal to the number of partitions of n into parts $\equiv \pm 2, \pm 3, \pm 4, \pm 5, \pm 6, \pm 7 \pmod 20$. The companion theorem proves that the number of partitions of an integer n into parts where even parts may not be repeated, where odd parts $> 1$ occur only if an adjacent even part occurs, and where 1’s occur arbitrarily is equal to the number of partitions of n into parts $\equiv \pm 1, \pm 2, \pm 5, \pm 6, \pm 8, \pm 9 \pmod 20$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 214 (1975), 95-111
  • MSC: Primary 10A45
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0414480-9
  • MathSciNet review: 0414480