Pure O-Sequences and Matroid h-Vectors
We study Stanley’s long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2014
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| Online Access: | http://hdl.handle.net/1721.1/85616 |
| _version_ | 1826211610073497600 |
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| author | Ha, Huy Tai Stokes, Erik Zanello, Fabrizio |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ha, Huy Tai Stokes, Erik Zanello, Fabrizio |
| author_sort | Ha, Huy Tai |
| collection | MIT |
| description | We study Stanley’s long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley’s conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley’s conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators. |
| first_indexed | 2024-09-23T15:08:42Z |
| format | Article |
| id | mit-1721.1/85616 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:08:42Z |
| publishDate | 2014 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/856162022-10-02T00:53:08Z Pure O-Sequences and Matroid h-Vectors Ha, Huy Tai Stokes, Erik Zanello, Fabrizio Massachusetts Institute of Technology. Department of Mathematics Zanello, Fabrizio Zanello, Fabrizio We study Stanley’s long-standing conjecture that the h-vectors of matroid simplicial complexes are pure O-sequences. Our method consists of a new and more abstract approach, which shifts the focus from working on constructing suitable artinian level monomial ideals, as often done in the past, to the study of properties of pure O-sequences. We propose a conjecture on pure O-sequences and settle it in small socle degrees. This allows us to prove Stanley’s conjecture for all matroids of rank 3. At the end of the paper, using our method, we discuss a first possible approach to Stanley’s conjecture in full generality. Our technical work on pure O-sequences also uses very recent results of the third author and collaborators. 2014-03-14T14:53:41Z 2014-03-14T14:53:41Z 2013-05 2011-01 Article http://purl.org/eprint/type/JournalArticle 0218-0006 0219-3094 http://hdl.handle.net/1721.1/85616 Ha, Huy Tai, Erik Stokes, and Fabrizio Zanello. “Pure O-Sequences and Matroid h-Vectors.” Ann. Comb. 17, no. 3 (September 2013): 495–508. en_US http://dx.doi.org/10.1007/s00026-013-0193-6 Annals 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 Springer-Verlag Zanello |
| spellingShingle | Ha, Huy Tai Stokes, Erik Zanello, Fabrizio Pure O-Sequences and Matroid h-Vectors |
| title | Pure O-Sequences and Matroid h-Vectors |
| title_full | Pure O-Sequences and Matroid h-Vectors |
| title_fullStr | Pure O-Sequences and Matroid h-Vectors |
| title_full_unstemmed | Pure O-Sequences and Matroid h-Vectors |
| title_short | Pure O-Sequences and Matroid h-Vectors |
| title_sort | pure o sequences and matroid h vectors |
| url | http://hdl.handle.net/1721.1/85616 |
| work_keys_str_mv | AT hahuytai pureosequencesandmatroidhvectors AT stokeserik pureosequencesandmatroidhvectors AT zanellofabrizio pureosequencesandmatroidhvectors |