The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions
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,...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2017
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| Online Access: | http://hdl.handle.net/1721.1/106353 https://orcid.org/0000-0003-3123-8241 |
| _version_ | 1826189607682703360 |
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| author | Zanello, Fabrizio Stanley, Richard P |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zanello, Fabrizio Stanley, Richard P |
| author_sort | Zanello, Fabrizio |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:18:19Z |
| format | Article |
| id | mit-1721.1/106353 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:18:19Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/1063532022-09-30T08:55:34Z The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions Zanello, Fabrizio Stanley, Richard P Massachusetts Institute of Technology. Department of Mathematics Stanley, Richard P 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. 2017-01-12T15:22:03Z 2017-01-12T15:22:03Z 2015-03 2013-12 Article http://purl.org/eprint/type/JournalArticle 0895-4801 1095-7146 http://hdl.handle.net/1721.1/106353 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 https://orcid.org/0000-0003-3123-8241 en_US http://dx.doi.org/10.1137/130950318 SIAM Journal on Discrete Mathematics 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. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Zanello, Fabrizio Stanley, Richard P The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title | The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title_full | The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title_fullStr | The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title_full_unstemmed | The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title_short | The Catalan Case of Armstrong's Conjecture on Simultaneous Core Partitions |
| title_sort | catalan case of armstrong s conjecture on simultaneous core partitions |
| url | http://hdl.handle.net/1721.1/106353 https://orcid.org/0000-0003-3123-8241 |
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