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arXiv · 1006.4081

Anti-lecture Hall Compositions and Overpartitions

William Y. C. Chen·Doris D. M. Sang·Diane Y. H. Shi
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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 $0,\pm 1$ 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 Rogers-Ramanujan 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.

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William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi. 2010-06-21. Anti-lecture Hall Compositions and Overpartitions. https://arxiv.org/abs/1006.4081

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