A Multi-Set Identity for Partitions

Details A Multi-Set Identity for Partitions A Multi-Set Identity for Partitions

2009-09-18

arxiv.org/abs/0909.3459v2

Mathematics

Combinatorics

4 pages, an on-line figure in http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/TemunaFerrers.html

Scientific paper

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.

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