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JCT
2011

Anti-lecture hall compositions and overpartitions

9 years 1 months ago
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
William Y. C. Chen, Doris D. M. Sang, Diane Y. H.
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where JCT
Authors William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
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