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Determining if a simple quiver is orientable
I’m trying to figure out if a simple quiver $ Q=(Q_0,Q_1,s,t) $ is orientable. By a “simple” quiver I mean that the quiver has only unoriented loops (cycles). The cycles are enumerated by a field $\sigma : Q_1 \to \mathbb{N} \cup \{0\} $.
For the cycles of length $ \sigma(a) = 2 $ I know if the cycle vanishes it’s orientable, because there is exactly one orientation of the quiver for each vanishing cycle.
For cycles of length $ \sigma(a) = 1 $ it is easy to see that any orientable quiver must have even number of vertices, for example: the cycle cannot enter the vertex $ t $, so it has to pass through two vertices. Thus if an orientable quiver has an odd number of vertices, $ \sigma(a) = 1 $, it is not orientable.
For cycles of length $ \sigma(a) \geq 3 $ it is not easy to see why the same reasoning can be applied.
For example, consider $ Q = (\{0,1,2,3,4\},\{(0,1),(1,2),(2,0),(2,3),(3,4)\},(4,0)) $. The only vanishing cycle is $ C_3 = (4,0) $, and it passes through $ (3
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Как сделать в форме нажатие по одной кнопке (без второй)?
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Нужно использовать стандартные библиотеки HTML5. К примеру, например, для кнопки
нужно добавить следующие атрибуты:
data-prefix=”button_”
data-suffix=”_on”
Пример:
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