Actions and Identities on Set Partitions
A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of A[superscript n] on the set of A-labeled partit...
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| Format: | Article |
| Language: | en_US |
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Electronic Journal of Combinatorics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89801 |
| _version_ | 1826204250588315648 |
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| author | Marberg, Eric |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Marberg, Eric |
| author_sort | Marberg, Eric |
| collection | MIT |
| description | A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of A[superscript n] on the set of A-labeled partitions of an (n+1)-set. By investigating the orbit decomposition of various families of set partitions under this action, we derive new combinatorial proofs of Coker's identity for the Narayana polynomial and its type B analogue, and establish a number of other related identities. In return, we also prove some enumerative results concerning André and Neto's supercharacter theories of type B and D. |
| first_indexed | 2024-09-23T12:51:20Z |
| format | Article |
| id | mit-1721.1/89801 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:51:20Z |
| publishDate | 2014 |
| publisher | Electronic Journal of Combinatorics |
| record_format | dspace |
| spelling | mit-1721.1/898012022-10-01T11:31:09Z Actions and Identities on Set Partitions Marberg, Eric Massachusetts Institute of Technology. Department of Mathematics Marberg, Eric A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of A[superscript n] on the set of A-labeled partitions of an (n+1)-set. By investigating the orbit decomposition of various families of set partitions under this action, we derive new combinatorial proofs of Coker's identity for the Narayana polynomial and its type B analogue, and establish a number of other related identities. In return, we also prove some enumerative results concerning André and Neto's supercharacter theories of type B and D. 2014-09-18T16:03:03Z 2014-09-18T16:03:03Z 2012-01 2011-09 Article http://purl.org/eprint/type/JournalArticle 1077-8926 http://hdl.handle.net/1721.1/89801 Marberg, Eric. "Actions and Identities on Set Partitions." Electronic Journal of Combinatorics, Volume 19, Issue 1 (2012). en_US http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p28 Electronic Journal of Combinatorics 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 Electronic Journal of Combinatorics Electronic Journal of Combinatorics |
| spellingShingle | Marberg, Eric Actions and Identities on Set Partitions |
| title | Actions and Identities on Set Partitions |
| title_full | Actions and Identities on Set Partitions |
| title_fullStr | Actions and Identities on Set Partitions |
| title_full_unstemmed | Actions and Identities on Set Partitions |
| title_short | Actions and Identities on Set Partitions |
| title_sort | actions and identities on set partitions |
| url | http://hdl.handle.net/1721.1/89801 |
| work_keys_str_mv | AT marbergeric actionsandidentitiesonsetpartitions |