The classification of serial posets with the non-negative quadratic Tits form being principal
Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets \(S\) satisfying the following conditions: (1) the quadratic Tits form \(q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}\) of \(S\) is non-negative; (2) \({\rm Ker}\,q...
Gespeichert in:
| Datum: | 2019 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2019
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-1393 |
|---|---|
| record_format |
ojs |
| spelling |
admjournalluguniveduua-article-13932019-07-14T19:54:06Z The classification of serial posets with the non-negative quadratic Tits form being principal Bondarenko, Vitaliy M. Styopochkina, Marina V. quiver, serial poset, principal poset, quadratic Tits form, semichain, minimax equivalence, one-side and two-side sums, minimax sum 15B33, 15A30 Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets \(S\) satisfying the following conditions: (1) the quadratic Tits form \(q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}\) of \(S\) is non-negative; (2) \({\rm Ker}\,q_S(z):=\{t\,|\, q_S(t)=0\}\) is an infinite cyclic group (equivalently, the corank of the symmetric matrix of \(q_S(z)\) is equal to \(1\)); (3) for any \(m\in\mathbb{N}\), there is a poset \(S(m)\supset S\) such that \(S(m)\) satisfies (1), (2) and \(|S(m)\setminus S|=m\). Lugansk National Taras Shevchenko University 2019-07-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393 Algebra and Discrete Mathematics; Vol 27, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1393/533 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2019-07-14T19:54:06Z |
| collection |
OJS |
| language |
English |
| topic |
quiver serial poset principal poset quadratic Tits form semichain minimax equivalence one-side and two-side sums minimax sum 15B33 15A30 |
| spellingShingle |
quiver serial poset principal poset quadratic Tits form semichain minimax equivalence one-side and two-side sums minimax sum 15B33 15A30 Bondarenko, Vitaliy M. Styopochkina, Marina V. The classification of serial posets with the non-negative quadratic Tits form being principal |
| topic_facet |
quiver serial poset principal poset quadratic Tits form semichain minimax equivalence one-side and two-side sums minimax sum 15B33 15A30 |
| format |
Article |
| author |
Bondarenko, Vitaliy M. Styopochkina, Marina V. |
| author_facet |
Bondarenko, Vitaliy M. Styopochkina, Marina V. |
| author_sort |
Bondarenko, Vitaliy M. |
| title |
The classification of serial posets with the non-negative quadratic Tits form being principal |
| title_short |
The classification of serial posets with the non-negative quadratic Tits form being principal |
| title_full |
The classification of serial posets with the non-negative quadratic Tits form being principal |
| title_fullStr |
The classification of serial posets with the non-negative quadratic Tits form being principal |
| title_full_unstemmed |
The classification of serial posets with the non-negative quadratic Tits form being principal |
| title_sort |
classification of serial posets with the non-negative quadratic tits form being principal |
| description |
Using (introduced by the first author) the method of (min, max)-equivalence, we classify all serial principal posets, i.e. the posets \(S\) satisfying the following conditions: (1) the quadratic Tits form \(q_S(z)\colon\mathbb{Z}^{|S|+1}\to\mathbb{Z}\) of \(S\) is non-negative; (2) \({\rm Ker}\,q_S(z):=\{t\,|\, q_S(t)=0\}\) is an infinite cyclic group (equivalently, the corank of the symmetric matrix of \(q_S(z)\) is equal to \(1\)); (3) for any \(m\in\mathbb{N}\), there is a poset \(S(m)\supset S\) such that \(S(m)\) satisfies (1), (2) and \(|S(m)\setminus S|=m\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1393 |
| work_keys_str_mv |
AT bondarenkovitaliym theclassificationofserialposetswiththenonnegativequadratictitsformbeingprincipal AT styopochkinamarinav theclassificationofserialposetswiththenonnegativequadratictitsformbeingprincipal AT bondarenkovitaliym classificationofserialposetswiththenonnegativequadratictitsformbeingprincipal AT styopochkinamarinav classificationofserialposetswiththenonnegativequadratictitsformbeingprincipal |
| first_indexed |
2025-12-02T15:38:50Z |
| last_indexed |
2025-12-02T15:38:50Z |
| _version_ |
1850412133756436480 |