Lecture hall theorems, q-series and truncated objects

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. The truncated lecture hall partitions are sequences (λ1, . . . , λk) such that λ1 n ≥ λ2 n − 1 ≥ . . . ≥ λk n − k + 1 ≥ 0 and we show that their generating function is : k ∑