Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes
We present extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes, providing a common generalization to the matroidal versions of the theorem due to Kalai and Meshulam, the ‘very colorful’ Helly theorem introduced by Arocha, Bárány, Bracho, Fabila and Montejano and the ‘sem...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000239/type/journal_article |
| _version_ | 1797229699085107200 |
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| author | Minki Kim Alan Lew |
| author_facet | Minki Kim Alan Lew |
| author_sort | Minki Kim |
| collection | DOAJ |
| description | We present extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes, providing a common generalization to the matroidal versions of the theorem due to Kalai and Meshulam, the ‘very colorful’ Helly theorem introduced by Arocha, Bárány, Bracho, Fabila and Montejano and the ‘semi-intersecting’ colorful Helly theorem proved by Montejano and Karasev. |
| first_indexed | 2024-04-24T15:16:44Z |
| format | Article |
| id | doaj.art-11807511665041b7b68a6625ff8e3bd7 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-24T15:16:44Z |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-11807511665041b7b68a6625ff8e3bd72024-04-02T09:10:58ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.23Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexesMinki Kim0https://orcid.org/0000-0002-9390-7255Alan Lew1https://orcid.org/0000-0002-2536-7859Division of Liberal Arts and Sciences, Gwangju Institute of Science and Technology (GIST), Gwangju, 61005, South KoreaDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA; E-mail:We present extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes, providing a common generalization to the matroidal versions of the theorem due to Kalai and Meshulam, the ‘very colorful’ Helly theorem introduced by Arocha, Bárány, Bracho, Fabila and Montejano and the ‘semi-intersecting’ colorful Helly theorem proved by Montejano and Karasev.https://www.cambridge.org/core/product/identifier/S2050509424000239/type/journal_article52A3505E4555U10 |
| spellingShingle | Minki Kim Alan Lew Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes Forum of Mathematics, Sigma 52A35 05E45 55U10 |
| title | Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes |
| title_full | Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes |
| title_fullStr | Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes |
| title_full_unstemmed | Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes |
| title_short | Extensions of the colorful Helly theorem for d-collapsible and d-Leray complexes |
| title_sort | extensions of the colorful helly theorem for d collapsible and d leray complexes |
| topic | 52A35 05E45 55U10 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424000239/type/journal_article |
| work_keys_str_mv | AT minkikim extensionsofthecolorfulhellytheoremfordcollapsibleanddleraycomplexes AT alanlew extensionsofthecolorfulhellytheoremfordcollapsibleanddleraycomplexes |