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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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/978 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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. |
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