We prove a conjecture of Thomas Lam that the face posets of stratified spaces of planar resistor networks are shellable. These posets are called uncrossing partial orders. This shellability result combines with Lam's previous result that these same posets are Eulerian to imply that they are CW posets, namely that they are face posets of regular CW complexes. Certain subposets of uncrossing partial orders are shown to be isomorphic to type A Bruhat order intervals; our shelling is shown to coincide on these intervals with a Bruhat order shelling which was constructed by Matthew Dyer using a reflection order.

Our shelling for uncrossing posets also yields an explicit shelling for each interval in the face posets of the edge product spaces of phylogenetic trees, namely in the Tuffley posets, by virtue of each interval in a Tuffley poset being isomorphic to an interval in an uncrossing poset. This yields a more explicit proof of the result of Gill, Linusson, Moulton and Steel that the CW decomposition of Moulton and Steel for the edge product space of phylogenetic trees is a regular CW decomposition.

我们证明了Thomas Lam的一个猜想，即平面电阻器网络的分层空间中的脸孔是可带壳的。这些位姿称为非交叉偏序。这种可炮击性结果与Lam先前的结果相结合，即这些相同的球体为欧拉式，表示它们是CW球体，即它们是常规CW配合物的面球体。某些不相交的偏序子子集与A型Bruhat阶区间是同构的。我们的脱壳在这些间隔上与Matthew Dyer使用反射顺序构造的Bruhat脱壳相吻合。

我们对不交叉姿势的脱壳还通过对不规则姿势中的每个间隔进行同构，对系统发育树的边缘乘积空间的面姿势中的每个间隔，即对不规则姿势中的每个间隔，都产生了明确的脱壳。 。这更清楚地证明了Gill，Linusson，Moulton和Steel的结果，即针对系统发育树的边缘乘积空间，Moulton和Steel的CW分解是规则的CW分解。