Classification of the almost positive posets
This paper introduces the notion of almost positive posets as non-negative ones that contain maximal positive subposets. Such posets include both positive posets and \(P\)-critical posets (minimal non-positive ones) which were described by the authors back in 2005. Almost positive posets also includ...
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Lugansk National Taras Shevchenko University
2025
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oai:ojs.admjournal.luguniv.edu.ua:article-23912025-04-13T15:32:01Z Classification of the almost positive posets Bondarenko, Vitaliy M. Styopochkina, Maryna V. almost positive poset, principal poset, \(P\)-critical poset, minimax equivalence, Tits quadratic form, minimax \(d\)-system of generators 06A07, 11E04 This paper introduces the notion of almost positive posets as non-negative ones that contain maximal positive subposets. Such posets include both positive posets and \(P\)-critical posets (minimal non-positive ones) which were described by the authors back in 2005. Almost positive posets also include principal posets in the sense of D. Simson. By definition, a non-negative poset \(S=\{1,\cdots, n;\, \preceq\}\) is principal if the kernel of its Tits quadratic form \(q_S(z)=q_S(z_0,z_1,\cdots,z_n)\), defined by the equality \({\rm Ker}\,q_S(z):=\{t\in \mathbb{Z}^{1+n}\,|\, q_S(t)=0\}\), is an infinite cyclic subgroup of \(\mathbb{Z}^{1+n}\). In 2019, the authors described all serial principal posets. This paper concludes the description of all almost positive posets. Lugansk National Taras Shevchenko University 2025-04-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2391 10.12958/adm2391 Algebra and Discrete Mathematics; Vol 39, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2391/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2391/1298 Copyright (c) 2025 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2025-04-13T15:32:01Z |
| collection |
OJS |
| language |
English |
| topic |
almost positive poset principal poset \(P\)-critical poset minimax equivalence Tits quadratic form minimax \(d\)-system of generators 06A07 11E04 |
| spellingShingle |
almost positive poset principal poset \(P\)-critical poset minimax equivalence Tits quadratic form minimax \(d\)-system of generators 06A07 11E04 Bondarenko, Vitaliy M. Styopochkina, Maryna V. Classification of the almost positive posets |
| topic_facet |
almost positive poset principal poset \(P\)-critical poset minimax equivalence Tits quadratic form minimax \(d\)-system of generators 06A07 11E04 |
| format |
Article |
| author |
Bondarenko, Vitaliy M. Styopochkina, Maryna V. |
| author_facet |
Bondarenko, Vitaliy M. Styopochkina, Maryna V. |
| author_sort |
Bondarenko, Vitaliy M. |
| title |
Classification of the almost positive posets |
| title_short |
Classification of the almost positive posets |
| title_full |
Classification of the almost positive posets |
| title_fullStr |
Classification of the almost positive posets |
| title_full_unstemmed |
Classification of the almost positive posets |
| title_sort |
classification of the almost positive posets |
| description |
This paper introduces the notion of almost positive posets as non-negative ones that contain maximal positive subposets. Such posets include both positive posets and \(P\)-critical posets (minimal non-positive ones) which were described by the authors back in 2005. Almost positive posets also include principal posets in the sense of D. Simson. By definition, a non-negative poset \(S=\{1,\cdots, n;\, \preceq\}\) is principal if the kernel of its Tits quadratic form \(q_S(z)=q_S(z_0,z_1,\cdots,z_n)\), defined by the equality \({\rm Ker}\,q_S(z):=\{t\in \mathbb{Z}^{1+n}\,|\, q_S(t)=0\}\), is an infinite cyclic subgroup of \(\mathbb{Z}^{1+n}\). In 2019, the authors described all serial principal posets. This paper concludes the description of all almost positive posets. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2025 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2391 |
| work_keys_str_mv |
AT bondarenkovitaliym classificationofthealmostpositiveposets AT styopochkinamarynav classificationofthealmostpositiveposets |
| first_indexed |
2025-07-17T10:33:39Z |
| last_indexed |
2025-07-17T10:33:39Z |
| _version_ |
1839314978423701504 |