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Lecture Hall Theorems, q-series and Truncated Objects

S. Corteel·C. D. Savage
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Abstract

We show here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture hall-type theorems for truncated objects. We compute their generating function and give two different multivariate refinements of these new results : the q-calculus approach gives (u,v,q)-refinements, while a completely different approach gives odd/even (x,y)-refinements. From this, we are able to give a combinatorial characterization of truncated lecture hall partitions and new finitizations of refinements of Euler's theorem.

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S. Corteel, C. D. Savage. 2003-09-05. Lecture Hall Theorems, q-series and Truncated Objects. https://arxiv.org/abs/math/0309108

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