The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions

Author(s)
Zanello, Fabrizio; Stanley, Richard P
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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.
Date issued
2015-03
URI
http://hdl.handle.net/1721.1/106353
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
0895-4801
1095-7146
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