A horizontal mesh algorithm for posets with positive Tits form
Following our paper [Fund. Inform. 136 (2015), 345--379], we define a~horizontal mesh algorithm that constructsa~$\widehat{\Phi}_I$-mesh translation quiver $\Gamma(\widehat{\CR}_I,\widehat{\Phi}_I)$ consisting of$\widehat{\Phi}_I$-orbits of the finite set $\widehat{\CR}_I=\{v\in\mathbb{Z}^I\; ;\;\...
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| Дата: | 2016 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/130 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-1302016-12-30T22:42:45Z A horizontal mesh algorithm for posets with positive Tits form Kaniecki, Mariusz Kosakowska, Justyna Malicki, Piotr Marczak, Grzegorz poset; combinatorial algorithm; Dynkin diagram; mesh geometry of roots; quadratic form 68R10; 05C50; 06A07; 15A63 Following our paper [Fund. Inform. 136 (2015), 345--379], we define a~horizontal mesh algorithm that constructsa~$\widehat{\Phi}_I$-mesh translation quiver $\Gamma(\widehat{\CR}_I,\widehat{\Phi}_I)$ consisting of$\widehat{\Phi}_I$-orbits of the finite set $\widehat{\CR}_I=\{v\in\mathbb{Z}^I\; ;\;\widehat{q}_I(v)=1\}$ of Tits roots of a~poset $I$ with positivedefinite Tits quadratic form $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$. Under the assumption that $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$ is positive definite, the algorithm constructs $\Gamma(\widehat{\CR}_I,\widehat{\Phi}_I)$ such that it is isomorphic with the $\widehat{\Phi}_D$-mesh translation quiver $\Gamma({\CR}_D,{\Phi}_D)$ of $\widehat{\Phi}_D$-orbits of the finite set ${\CR}_D$ of roots of a simply laced Dynkin quiver $D$ associated with $I$. Lugansk National Taras Shevchenko University 2016-12-31 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/130 Algebra and Discrete Mathematics; Vol 22, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/130/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2016-12-30T22:42:45Z |
| collection |
OJS |
| language |
English |
| topic |
poset combinatorial algorithm Dynkin diagram mesh geometry of roots quadratic form 68R10 05C50 06A07 15A63 |
| spellingShingle |
poset combinatorial algorithm Dynkin diagram mesh geometry of roots quadratic form 68R10 05C50 06A07 15A63 Kaniecki, Mariusz Kosakowska, Justyna Malicki, Piotr Marczak, Grzegorz A horizontal mesh algorithm for posets with positive Tits form |
| topic_facet |
poset combinatorial algorithm Dynkin diagram mesh geometry of roots quadratic form 68R10 05C50 06A07 15A63 |
| format |
Article |
| author |
Kaniecki, Mariusz Kosakowska, Justyna Malicki, Piotr Marczak, Grzegorz |
| author_facet |
Kaniecki, Mariusz Kosakowska, Justyna Malicki, Piotr Marczak, Grzegorz |
| author_sort |
Kaniecki, Mariusz |
| title |
A horizontal mesh algorithm for posets with positive Tits form |
| title_short |
A horizontal mesh algorithm for posets with positive Tits form |
| title_full |
A horizontal mesh algorithm for posets with positive Tits form |
| title_fullStr |
A horizontal mesh algorithm for posets with positive Tits form |
| title_full_unstemmed |
A horizontal mesh algorithm for posets with positive Tits form |
| title_sort |
horizontal mesh algorithm for posets with positive tits form |
| description |
Following our paper [Fund. Inform. 136 (2015), 345--379], we define a~horizontal mesh algorithm that constructsa~$\widehat{\Phi}_I$-mesh translation quiver $\Gamma(\widehat{\CR}_I,\widehat{\Phi}_I)$ consisting of$\widehat{\Phi}_I$-orbits of the finite set $\widehat{\CR}_I=\{v\in\mathbb{Z}^I\; ;\;\widehat{q}_I(v)=1\}$ of Tits roots of a~poset $I$ with positivedefinite Tits quadratic form $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$. Under the assumption that $\widehat q_I:\mathbb{Z}^I \to \mathbb{Z}$ is positive definite, the algorithm constructs $\Gamma(\widehat{\CR}_I,\widehat{\Phi}_I)$ such that it is isomorphic with the $\widehat{\Phi}_D$-mesh translation quiver $\Gamma({\CR}_D,{\Phi}_D)$ of $\widehat{\Phi}_D$-orbits of the finite set ${\CR}_D$ of roots of a simply laced Dynkin quiver $D$ associated with $I$. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/130 |
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