Abstract
We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.
Mathematics Subject Classification: 05A15 (05A17, 05A19, 05A30, 11P81, 11P82)
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Corteel, S., Savage, C.D., Sills, A.V. (2012). Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities. In: Alladi, K., Garvan, F. (eds) Partitions, q-Series, and Modular Forms. Developments in Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0028-8_6
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DOI: https://doi.org/10.1007/978-1-4614-0028-8_6
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