The Deodhar decomposition of the Grassmannian is a refinement of the Schubert, Richardson, and positroid stratifications of the Grassmannian. Go-diagrams are certain fillings of Ferrers diagrams with black stones, white stones, and pluses which index Deodhar components in the Grassmannian. We provide a series of corrective flips on diagrams which may be used to transform arbitrary fillings of Ferrers shapes with black stones, white stones, and pluses into a Go-diagram. This provides an extension of Lam and Williams’ Le-moves for transforming reduced diagrams into Le-diagrams to the context of non-reduced diagrams. Next, we address the question of describing when the closure of one Deodhar component is contained in the closure of another. We show that if one Go-diagram D is obtained from another \(D'\) by replacing certain stones with pluses, then applying corrective flips, that there is a containment of closures of the associated Deodhar components, \(\overline{{\mathcal {D}}'} \subset {\overline{{\mathcal {D}}}}\). Finally, we address the question of verifying whether an arbitrary filling of a Ferrers shape with black stones, white stones, and pluses is a Go-diagram. We show that no reasonable description of the class of Go-diagrams in terms of forbidden subdiagrams can exist by providing an injection from the set of valid Go-diagrams to the set of minimal forbidden subdiagrams for the class of Go-diagrams. In lieu of such a description, we offer an inductive characterization of the class of Go-diagrams.

中文翻译：

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Grassmannian的Deodhar分解的组合

Grassmannian的Deodhar分解是Schubert，Richardson的细化和Grassmannian的正弦分层。Go-diagrams是用黑色石头，白色石头和加号表示的Ferrers图的某些填充，这些图索引了Grassmannian中的Deodhar分量。我们在图表上提供了一系列的校正性翻转，可用于将带有黑色石头，白色石头和加号的Ferrers形状的任意填充转换成Go-diagram。这提供了Lam和Williams的Le-moves的扩展，用于将简化图转换为Le-diagrams到非简化图的上下文。接下来，我们要解决的问题是描述一个Deodhar组件的封闭何时包含在另一个组件的封闭中。我们表明，如果从另一个获得了一个Go-图D\（D'\），用加号替换某些石头，然后进行校正翻转，以控制相关的Deodhar组件的闭合，\（\ overline {{\ mathcal {D}}'} \ subset {\ overline {{\ mathcal {D}}}} \）。最后，我们解决了以下问题：验证用黑色石头，白色石头和加号任意填充Ferrers形状是否是Go-diagram。我们显示，通过提供从有效Go-图组到最小Go-图组的最小禁止子图组的注入，就不能存在关于禁止子图的Go-图类的合理描述。代替这种描述，我们提供了Go-gram类的归纳表征。