Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\)
We give a complete description of connected non-negative Dynkin type Dyn\(_I=\mathbb{E}_m\) posets and prove that the number of such posets is finite. Moreover, by means of computer assisted analysis, we give a complete Coxeter classification of this class and prove that the pair (Dyn\(_I=\mathbb{E}...
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| Date: | 2026 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2026
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2408 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543304825438208 |
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| author | Gąsiorek, Marcin |
| author_facet | Gąsiorek, Marcin |
| author_sort | Gąsiorek, Marcin |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2026-01-11T10:11:21Z |
| description | We give a complete description of connected non-negative Dynkin type Dyn\(_I=\mathbb{E}_m\) posets and prove that the number of such posets is finite. Moreover, by means of computer assisted analysis, we give a complete Coxeter classification of this class and prove that the pair (Dyn\(_I=\mathbb{E}_m,\) specc\(_I\)), where specc\(_I\subseteq\mathbb{C}\) denotes the Coxeter spectrum of \(I\), determines \(I\) uniquely, up to the strong Gram \(\mathbb{Z}\)-congruence. |
| first_indexed | 2026-02-08T08:01:06Z |
| format | Article |
| id | admjournalluguniveduua-article-2408 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:06Z |
| publishDate | 2026 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-24082026-01-11T10:11:21Z Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) Gąsiorek, Marcin non-negative poset, unit quadratic form, Coxeter-Dynkin type, Coxeter spectrum 06A07, 06A11, 11E04, 68W30 We give a complete description of connected non-negative Dynkin type Dyn\(_I=\mathbb{E}_m\) posets and prove that the number of such posets is finite. Moreover, by means of computer assisted analysis, we give a complete Coxeter classification of this class and prove that the pair (Dyn\(_I=\mathbb{E}_m,\) specc\(_I\)), where specc\(_I\subseteq\mathbb{C}\) denotes the Coxeter spectrum of \(I\), determines \(I\) uniquely, up to the strong Gram \(\mathbb{Z}\)-congruence. Lugansk National Taras Shevchenko University 2026-01-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2408 10.12958/adm2408 Algebra and Discrete Mathematics; Vol 40, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2408/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2408/1341 Copyright (c) 2026 Algebra and Discrete Mathematics |
| spellingShingle | non-negative poset unit quadratic form Coxeter-Dynkin type Coxeter spectrum 06A07 06A11 11E04 68W30 Gąsiorek, Marcin Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title | Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title_full | Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title_fullStr | Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title_full_unstemmed | Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title_short | Coxeter spectral classification of non-negative posets of Dynkin type \(\mathbb{E}_m\) |
| title_sort | coxeter spectral classification of non-negative posets of dynkin type \(\mathbb{e}_m\) |
| topic | non-negative poset unit quadratic form Coxeter-Dynkin type Coxeter spectrum 06A07 06A11 11E04 68W30 |
| topic_facet | non-negative poset unit quadratic form Coxeter-Dynkin type Coxeter spectrum 06A07 06A11 11E04 68W30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2408 |
| work_keys_str_mv | AT gasiorekmarcin coxeterspectralclassificationofnonnegativeposetsofdynkintypemathbbem |