This paper is concerned with a refined enumeration of anti-lecture hall compositions
with an upper bound on the first entry. It turns out this problem is related to
overpartition analogues of Roger-Ramanujan type identities, and a transformation
formula of Andrews. It is a little surprising that the upper bound on the
first entry corresponds to congruence restrictions on the parts of overpartitions.
We have used bijections as well as generating functions to
prove the main result. 


Editor:

George Andrews