Anti-lecture hall compositions and overpartitions

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 refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two RogersRamanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage. Keywords. Anti-lecture hall composition, Rogers-Ramanujan identity, overpartition, Durfee dissection AMS Subject Classification. 05A17, 11P84

• Type: Journal
• Year: 2011
• Where: JCT
• Authors: William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
• Keywords: Anti-lecture Hall, Anti-lecture Hall Composition, JCT 2011, Rogers-Ramanujan Identity