On the refined lecture hall theorem

A lecture hall partition of length n is a sequence (λ1,λ2, …, λn) of nonnegative integers satisfying 0⩽λ1/1⩽⋯⩽λn/n. M. Bousquet-Mélou and K. Eriksson showed that there is an one to one correspondence between the set of all lecture hall partitions of length n and the set of all partitions with distinct parts between 1 and n, and possibly multiple parts between n+1 and 2n. In this paper, we construct a bijection which is an identity mapping in the limiting case.