仿射Deodhar图的组合学
The Combinatorics of Affine Deodhar Diagrams
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中文总结 AI 辅助
研究仿射Deodhar图，它由有界仿射置换和格路径索引，通过构造几类仿射Deogram之间的双射，为有限域上开放正roid簇点数恒等式提供组合证明，扩展了Deodhar图构造到仿射补丁。
中文摘要 AI 辅助
Deodhar图提供了一种组合方式来计算有限域上开放正roid簇的点数。我们引入了仿射Deodhar图，将此构造扩展到开放正roid簇的仿射补丁。这些图由有界仿射置换和格路径索引，这种额外的灵活性使其对递归双射特别有用。受与Dyck路径、开放正roid簇及其簇结构的联系启发，我们构造了几类仿射Deogram之间的双射。这些双射给出了先前从几何同构已知的点数恒等式的组合证明。
英文摘要
Deodhar diagrams give a combinatorial way to compute point counts of open positroid varieties over finite fields. We introduce affine Deodhar diagrams, which extend this construction to affine patches of open positroid varieties. These diagrams are indexed by a bounded affine permutation together with a lattice path, and this extra flexibility makes them especially useful for recursive bijections. Motivated by connections with Dyck paths, open positroid varieties, and their cluster structure, we construct bijections between several classes of affine Deograms. These bijections give combinatorial proofs of point-count identities that were previously known from geometric isomorphisms.
