A Recursive Relation for Bipartition Numbers

2024/06/21 by Yen-Chi Roger Lin, Lin, Yen-Chi Roger, Shu-Yen Pan +1
Computer Science · #05A17 #11P87 #20C33 #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2406.14851

openalex publication_date 2024/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a recursive relation for the bipartition number p₂(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.

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