Coxeter群与Billey-Postnikov分解
Coxeter groups and Billey-Postnikov decompositions
AI总结：
本文综述了Billey-Postnikov分解在光滑Schubert簇分类计数、反演超平面排列及排列模式避免等领域的应用。
摘要：
在本章中，我们概述Billey-Postnikov（BP）分解，该分解已成为理解Schubert簇的几何与组合学的重要工具。BP分解是Coxeter群元素的因子分解，具有许多与Bruhat偏序相关的优良性质。它们在光滑Schubert簇的分类与计数中发挥了重要作用。它们还被用于反演超平面排列和排列模式避免的研究。我们综述了其中许多应用。
英文摘要：
In this chapter, we give an overview of Billey-Postnikov (BP) decompositions which have become an important tool for understanding the geometry and combinatorics of Schubert varieties. BP decompositions are factorizations of Coxeter group elements with many nice properties in relation to Bruhat partial order. They have played an important role in the classification and enumeration of smooth Schubert varieties. They have also been used in the study of inversion hyperplane arrangements and permutation pattern avoidance. We survey many of these applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
