论文标题
Amplituhedron交叉和绕组数字
The amplituhedron crossing and winding numbers
论文作者
论文摘要
在\ cite {arkani2018unwinding}中，arkani-hamed，thomas和trnka根据$ m $的奇偶校验，对树amplituhedron $ \ ampli $进行了两个猜想的描述。当$ m $均匀时，描述涉及绕组编号，当$ m $奇怪时，描述涉及交叉数字。在本文中，我们证明，如果Amplituhedron地图的Amplituhedron点位于正Grassmannian的图像中，那么根据$ M $的奇偶校验，它可以满足绕组或交叉描述。当$ m = 2 $时，我们还证明了另一个方向：满足绕组描述的点在Amplituhedron内部。
In \cite{arkani2018unwinding}, Arkani-Hamed, Thomas and Trnka formulated two conjectural descriptions of the tree amplituhedron $\ampli$ depending on the parity of $m$. When $m$ is even, the description involves the winding number and when $m$ is odd the description involves the crossing number. In this paper, we prove that if a point of the amplituhedron is in the image of the positive Grassmannian by the amplituhedron map, then it satisfies the winding or crossing descriptions depending on the parity of $m$. When $m=2$, we also prove the other direction: a point satisfying the winding description is inside the amplituhedron.
