The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions
Name
The catalan case.pdf
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247.24 KB
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Adobe PDF
Checksum (MD5)
cd5f68d0b757092dec1ea4a3573127cb
Author(s)
Zanello, Fabrizio
Stanley, Richard P
Date Issued
March 2015
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Stanley, Richard P., and Fabrizio Zanello. “The Catalan Case of Armstrong’s Conjecture on Simultaneous Core Partitions.” SIAM Journal on Discrete Mathematics 29.1 (2015): 658–666. © 2015 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
A beautiful recent conjecture of Armstrong predicts the average size of a partition that is simultaneously an s-core and a t-core, where s and t are coprime. Our goal is to prove this conjecture when t = s + 1. These simultaneous (s, s + 1)-core partitions, which are enumerated by
Catalan numbers, have average size (s+1 over 3)/2.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/130950318
