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

Jineon Baek; Hayan Nam; Myungjun Yu

doi:10.1016/j.disc.2018.01.020

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

Jineon Baek, Hayan Nam, Myungjun Yu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1294-1300
Number of pages	7
Journal	Discrete Mathematics
Volume	341
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2018.01.020
Publication status	Published - 2018 May

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2018.01.020

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abstract = "Amdeberhan conjectured that the number of (s,s+2)-core partitions with distinct parts for an odd integer s is 2s−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.",

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

Abstract

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