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Partition theorems related to some identities of Rogers and Watson


Author: Willard G. Connor
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
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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

DOI: https://doi.org/10.1090/S0002-9947-1975-0414480-9
Keywords: Partitions, q-series identities, Rogers-Ramanujan identities, generalized Rogers-Ramanujan identities, frequency of parts, Selberg's equation
Article copyright: © Copyright 1975 American Mathematical Society

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