When Does the Set of (a, b, c)-Core Partitions Have a Unique Maximal Element?
Name
Aggarwal-2015-When does the set.pdf
Size
285.32 KB
Format
Adobe PDF
Checksum (MD5)
978ae01f85d4333368269e0456e3a96e
Author(s)
Aggarwal, Amol
Date Issued
May 2015
Journal
Electronic Journal of Combinatorics
Publisher
European Mathematical Information Service (EMIS)
Citation
Aggarwal, Amol. "When Does the Set of (a, b, c)-Core Partitions Have a Unique Maximal Element?" The Electronic Journal of Combinatorics 22(2) (2015), #P2.31
Version
Final published version
Abstract
In 2007, Olsson and Stanton gave an explicit form for the largest (a; b)-core partition, for any relatively prime positive integers a and b, and asked whether there exists an (a; b)-core that contains all other (a; b)-cores as subpartitions; this question was answered in the affirmative first by Vandehey and later by Fayers independently. In this paper we investigate a generalization of this question, which was originally posed by Fayers: for what triples of positive integers (a; b; c) does there exist an (a; b; c)-core that contains all other (a; b; c)-cores as subpartitions? We completely answer this question when a, b, and c are pairwise relatively prime; we then use this to generalize the result of Olsson and Stanton.
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/10.37236/4773
