Minimax sums of posets and the quadratic Tits form
Let \(S\) be an infinite poset (partially ordered set) and \(\mathbb{Z}_0^{S\cup{0}}\) the subset of the cartesian product \(\mathbb{Z}^{S\cup{0}}\) consisting of all vectors \(z=(z_i)\) with finite number of nonzero coordinates. We call the quadratic Tits form of \(S\) (by analogy with the case of...
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-9782018-05-14T08:03:48Z Minimax sums of posets and the quadratic Tits form Bondarenko, Vitalij M. Polishchuk, Andrej M. poset, minimax sum, the rank of a sum, the Tits form 15A, 16G Let \(S\) be an infinite poset (partially ordered set) and \(\mathbb{Z}_0^{S\cup{0}}\) the subset of the cartesian product \(\mathbb{Z}^{S\cup{0}}\) consisting of all vectors \(z=(z_i)\) with finite number of nonzero coordinates. We call the quadratic Tits form of \(S\) (by analogy with the case of a finite poset) the form \(q_S:\mathbb{Z}_0^{S\cup{0}} \to \mathbb{Z}\) defined by the equality \(q_S(z)=z_0^2+\sum_{i\in S} z_i^2 +\sum_{i<j, i,j\in S}z_iz_j-z_0\sum_{i\in S}z_i\). In this paper we study the structure of infinite posets with positive Tits form. In particular, there arise posets of specific form which we call minimax sums of posets. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/978 Algebra and Discrete Mathematics; Vol 3, No 1 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/978/507 Copyright (c) 2018 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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English |
| topic |
poset minimax sum the rank of a sum the Tits form 15A 16G |
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poset minimax sum the rank of a sum the Tits form 15A 16G Bondarenko, Vitalij M. Polishchuk, Andrej M. Minimax sums of posets and the quadratic Tits form |
| topic_facet |
poset minimax sum the rank of a sum the Tits form 15A 16G |
| format |
Article |
| author |
Bondarenko, Vitalij M. Polishchuk, Andrej M. |
| author_facet |
Bondarenko, Vitalij M. Polishchuk, Andrej M. |
| author_sort |
Bondarenko, Vitalij M. |
| title |
Minimax sums of posets and the quadratic Tits form |
| title_short |
Minimax sums of posets and the quadratic Tits form |
| title_full |
Minimax sums of posets and the quadratic Tits form |
| title_fullStr |
Minimax sums of posets and the quadratic Tits form |
| title_full_unstemmed |
Minimax sums of posets and the quadratic Tits form |
| title_sort |
minimax sums of posets and the quadratic tits form |
| description |
Let \(S\) be an infinite poset (partially ordered set) and \(\mathbb{Z}_0^{S\cup{0}}\) the subset of the cartesian product \(\mathbb{Z}^{S\cup{0}}\) consisting of all vectors \(z=(z_i)\) with finite number of nonzero coordinates. We call the quadratic Tits form of \(S\) (by analogy with the case of a finite poset) the form \(q_S:\mathbb{Z}_0^{S\cup{0}} \to \mathbb{Z}\) defined by the equality \(q_S(z)=z_0^2+\sum_{i\in S} z_i^2 +\sum_{i<j, i,j\in S}z_iz_j-z_0\sum_{i\in S}z_i\). In this paper we study the structure of infinite posets with positive Tits form. In particular, there arise posets of specific form which we call minimax sums of posets. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/978 |
| work_keys_str_mv |
AT bondarenkovitalijm minimaxsumsofposetsandthequadratictitsform AT polishchukandrejm minimaxsumsofposetsandthequadratictitsform |
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2024-04-12T06:26:24Z |
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2024-04-12T06:26:24Z |
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1796109169644797952 |