(Anti)-Lecture Hall, -series and Truncated  Objects

Sylvie Corteel ^[1]

CNRS-Universit Versailles, France

Sylvie.Corteel@prism.uvsq.fr

Abstract.      Full Text PDF
 

Lecture Hall partitions were introduced by Bousquet-Melou and Eriksson in 1996. Proofs of the Lecture Hall theorems were done using algebra and/or bijections. We show here that the refined theorem for Lecture Hall partitions can be obtained using -series identities. It is a straightforward consequence of one of the -Chu-Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture hall-type theorems for truncated objects. We define truncated lecture hall partitions and compute their generating function. From this, we are able to give a combinatorial characterization of truncated lecture hall partitions and new finitizations of refinements of Euler’s theorem. We also show that the same kinds of results hold for anti-lecture hall compositions.

 

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^[1] This is joint work with Carla Savage.