Anti-lecture hall compositions and overpartitions

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Chen, William Y. C.¹  Sang, Doris D. M.¹  Shi, Diane Y. H.¹ 

[1] Nankai Univ, LPMC TJKLC, Ctr Combinator, Tianjin 300071, Peoples R China

关键词: Anti-lecture hall composition;    Rogers-Ramanujan type identity;    Overpartition;    Durfee dissection;   

DOI  :  10.1016/j.jcta.2010.11.021

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free