A bijective proof of Amdeberhan's conjecture on the number of (s, s+2)-core partitions with distinct parts

2017/05/07 by Jineon Baek, Hayan Nam, Baek, Jineon +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1705.02691

openalex publication_date 2017/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Amdeberhan conjectured that the number of (s,s+2)-core partitions with distinct parts for an odd integer s is 2^s-1. This conjecture was first proved by Yan, Qin, Jin and Zhou, then subsequently by Zaleski and Zeilberger. Since the formula for the number of such core partitions is so simple one can hope for a bijective proof. We give the first direct bijective proof of this fact by establishing a bijection between the set of (s, s+2)-core partitions with distinct parts and a set of lattice paths.

Citations

• Theorems, Problems and Conjectures

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