2003/09/05 by Sylvie Corteel, S. Corteel, Corteel, S. +3
Mathematics · Physics and Astronomy · #05A17 05A15 05A30 33D15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:05A17 #msc:05A30 #msc:33D15
paper · pdf · doi:10.48550/arxiv.math/0309108
arxiv created 2003/09/05 · openalex publication_date 2003/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.