A lecture hall partition of length n is an integer sequence λ = (λ1,..., λn) satisfying 0 ≤ λ1/1 ≤ λ2/2 ≤ ... ≤ λn/n. (1) Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n of a positive integer N whose alternating sum is k equals the number of partitions of N into k odd parts less than 2n. We prove the fact by a natural combinatorial bijection. This bijection, though defined differently, is essentially the same as one of the bijections found by Bousquet-Mélou and Eriksson.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory