Mathematics – Combinatorics
Scientific paper
2010-06-21
Mathematics
Combinatorics
16 pages
Scientific paper
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.
Chen William Y. C.
Sang Doris D. M.
Shi Diane Y. H.
No associations
LandOfFree
Anti-lecture Hall Compositions and Overpartitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Anti-lecture Hall Compositions and Overpartitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anti-lecture Hall Compositions and Overpartitions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-601668