裤子图上的稳定线性方程是有理的
Stable Lengths on the pants graph are rational
摘要：
对于裤子图，很少有人知道测地线的行为，而不是准测地线。Brock-Masur-Minsky证明了连接端点的测地线或测线段满足有界组合条件，例如伪Anosov的稳定/不稳定叠层，都有界组合，\textit{outside of annuli}。在本文中，它是存在的测地线，也有界组合环内。这些测地线被证明具有有限性质类似于那些紧测地线在复杂的曲线，从合理性的稳定长度的伪Anosovs的裤子图，然后遵循从参数的Bowditch的曲线复杂。
英文摘要：
For the pants graph, there is little known about the behaviour of geodesics, as opposed to quasigeodesics. Brock-Masur-Minsky showed that geodesics or geodesic segments connecting endpoints satisfying a bounded combinatorics condition, such as the stable/unstable laminations of a pseudo-Anosov, all have bounded combinatorics, \textit{outside of annuli}. In this paper it is shown that there exist geodesics that also have bounded combinatorics within annuli. These geodesics are shown to have finiteness properties analogous to those of tight geodesics in the complex of curves, from which rationality of stable lengths of pseudo-Anosovs acting on the pants graph then follows from the arguments of Bowditch for the curve complex.
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