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Presentation
Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities
Proceedings of the Conference on Partitions, q-Series, and Modular Forms
  • Sylvie Corteel, Université Paris-Sud
  • Carla D. Savage, North Carolina State University
  • Andrew Sills, Georgia Southern University
Document Type
Conference Proceeding
Publication Date
3-12-2012
DOI
10.1007/978-1-4614-0028-8_6
ISBN
978-1-4614-0027-1
Disciplines
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.

Comments

This is a preprint of the final published article available at Developments in Mathematics.

Citation Information
Sylvie Corteel, Carla D. Savage and Andrew Sills. "Lecture Hall Sequences, q-Series, and Asymmetric Partition Identities" New York, NYProceedings of the Conference on Partitions, q-Series, and Modular Forms Vol. 23 (2012) p. 53 - 68
Available at: http://works.bepress.com/andrew_sills/38/