A Multi-Set Identity for Partitions
Combinatorics
2009-09-22 v2
Abstract
We prove that the multiset {(RightArmLength,LeftArmLength)} ranging over all cells of all Ferrers diagrams with n cells equals the multiset {(RightArmLength,LegLength)} ranging over all cells of all Ferrers diagrams with n cells, thereby refining a multi-set identity proved by C. Bessenrodt and by Bacher and L. Manivel. Added In revised version: Guo-Niu Han kindly pointed out to us that our main result is contained in reference [B.H] of the present article.
Cite
@article{arxiv.0909.3459,
title = {A Multi-Set Identity for Partitions},
author = {Amitai Regev and Doron Zeilberger},
journal= {arXiv preprint arXiv:0909.3459},
year = {2009}
}
Comments
4 pages, an on-line figure in http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/TemunaFerrers.html