descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2018Embargo end date: 01 Jan 2017 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 341, pages 1,294-1,300 (issn: 0012-365X,

Authors: Jineon Baek; Hayan Nam; Myungjun Yu;

doi: 10.1016/j.disc.2018.01.020 , 10.48550/arxiv.1705.02691

arXiv: http://arxiv.org/abs/1705.02691

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

- Summary
- Subjects
- Related research
  (1)
- Metrics

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.

9 pages

Related Organizations

University of California, Irvine
United States
University of Michigan–Flint
United States
University of Michigan–Ann Arbor
United States

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

1 Research products, page 1 of 1

THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND
2012IsAmongTopNSimilarDocuments

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	7
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%