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Алгебра и анализ, 2014, том 26, выпуск 2, страницы 216–228
(Mi aa1382)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Статьи
Tropical semimodules of dimension two
Ya. Shitov National Research University Higher School of Economics, Myasnitskaya Ulitsa, 20, 101000, Moscow, Russia
Аннотация:
The tropical arithmetic operations on $\mathbb R$ are defined as $a\oplus b=\min\{a,b\}$ and $a\otimes b=a+b$. In the paper, the concept of a semimodule is discussed, which is rather ill-behaved in tropical mathematics. The semimodules $S\subset\mathbb R^n$ having topological dimension two are studied and it is shown that any such $S$ has a finite weak dimension not exceeding $n$. For a fixed $k$, a polynomial time algorithm is constructed that decides whether $S$ is contained in some tropical semimodule of weak dimension $k$ or not. This result provides a solution of a problem that has been open for eight years.
Ключевые слова:
tropical mathematics, linear algebra, computational complexity.
Поступила в редакцию: 27.06.2013
Образец цитирования:
Ya. Shitov, “Tropical semimodules of dimension two”, Алгебра и анализ, 26:2 (2014), 216–228; St. Petersburg Math. J., 26:2 (2015), 341–350
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1382 https://www.mathnet.ru/rus/aa/v26/i2/p216
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Страница аннотации: | 359 | PDF полного текста: | 65 | Список литературы: | 47 | Первая страница: | 26 |
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