A Recursive Relation for Bipartition Numbers

We establish a recursive relation for the bipartition number \(p_2(n)\) which might be regarded as an analogue of Euler's recursive relation for the partition number \(p(n)\). Two proofs of the main result are proved in this article. The first one is using the generating function, and the secon...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Yen-Chi, Roger Lin, Shu-Yen, Pan
Format: Article
Language:English
Online Access:Get full text
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Summary:We establish a recursive relation for the bipartition number \(p_2(n)\) which might be regarded as an analogue of Euler's recursive relation for the partition number \(p(n)\). Two proofs of the main result are proved in this article. The first one is using the generating function, and the second one is using combinatoric objects (called ``symbols'') created by Lusztig for studying representation theory of finite classical groups.
ISSN:2331-8422