The topology of the external activity complex of a matroid
We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal ord...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6355/pdf |
| _version_ | 1797270198739271680 |
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| author | Federico Ardila Federico Castillo Jose Samper |
| author_facet | Federico Ardila Federico Castillo Jose Samper |
| author_sort | Federico Ardila |
| collection | DOAJ |
| description | We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same h-vector. We prove that, after removing its cone points, the external activity complex is contractible if M contains U3,1 as a minor, and a sphere otherwise. |
| first_indexed | 2024-04-25T02:00:28Z |
| format | Article |
| id | doaj.art-4e79cb56a27a4dcd989b0fc6c94318eb |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:28Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-4e79cb56a27a4dcd989b0fc6c94318eb2024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63556355The topology of the external activity complex of a matroidFederico Ardila0Federico Castillo1Jose Samper2San Francisco State UniversityUniversity of California [Davis]University of Washington [Seattle]We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of Las Vergnas's external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of Las Vergnas's internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same h-vector. We prove that, after removing its cone points, the external activity complex is contractible if M contains U3,1 as a minor, and a sphere otherwise.https://dmtcs.episciences.org/6355/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Federico Ardila Federico Castillo Jose Samper The topology of the external activity complex of a matroid Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | The topology of the external activity complex of a matroid |
| title_full | The topology of the external activity complex of a matroid |
| title_fullStr | The topology of the external activity complex of a matroid |
| title_full_unstemmed | The topology of the external activity complex of a matroid |
| title_short | The topology of the external activity complex of a matroid |
| title_sort | topology of the external activity complex of a matroid |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6355/pdf |
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