@**article**{RISC5376,author = {W.Y.C.Chen and D.D.M.Sang and Diane Y.H. Shi},

title = {{ Anti-lecture hall compositions and overpartitions}},

language = {english},

abstract = {We show that the number of anti-lecture hall compositions of n
with the first entry not exceeding k − 2 equals the number of
overpartitions of n with non-overlined parts not congruent to 0,±1
modulo k. This identity can be considered as a finite version
of the anti-lecture hall theorem of Corteel and Savage. To prove
this result, we find two Rogers–Ramanujan type identities for
overpartitions which are analogous to the Rogers–Ramanujan type
identities due to Andrews. When k is odd, we give another proof
by using the bijections of Corteel and Savage for the anti-lecture
hall theorem and the generalized Rogers–Ramanujan identity also
due to Andrews.},

journal = {J.Combin. Theory, Ser. A.},

volume = {118},

number = {4},

pages = {1451--1464},

isbn_issn = {0097-3165},

year = {2011},

refereed = {yes},

keywords = {Anti-lecture hall composition, Rogers–Ramanujan type identity, Overpartition, Durfee dissection},

length = {14}

}