## 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