Sorting orders, subword complexes, Bruhat order and total positivity

Bruhat intervals, subword complexes and brick polyhedra for finite Coxeter groups

We study the interplay between the discrete geometry of Bruhat poset intervals and subword complexes of finite Coxeter systems. We establish connections between the cones generated by cover labels for Bruhat intervals and of root configurations for subword complexes, culminating in the notion of brick polyhedra for general subword complexes.

Bruhat order and graph structures of lower intervals in Coxeter groups

We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded posets, and two-sided quotients altogether. For this purpose, we introduce some new ideas, quotient lower intervals and quotient Bruhat graphs.

子词计数直到堆排序等价

Subword enumeration up to stack-sorting equivalence

本文探讨了堆排序等价下的子词计数，通过tortoise和hare操作扩展了无限序列的abelian复杂度函数，并应用于纸折叠词和图灵-莫尔斯词，揭示了堆排序与词组合学的交叉联系。

The sorting order on a Coxeter group

Let $(W,S)$ be an arbitrary Coxeter system. For each word $ω$ in the generators we define a partial order--called the {\sf $ω$-sorting order}--on the set of group elements $W_ω\subseteq W$ that occur as subwords of $ω$. We show that the $ω$-sorting order is a supersolvable join-distributive lattice and that it is strictly between the weak and Bruhat orders on the group. Moreover, the $ω$-sorting order is a "maximal lattice" in the sense that the addition of any collection of Bruhat covers results in a nonlattice. Along the way we define a class of structures called {\sf supersolvable antimatro…

中间序：弱序与Bruhat序之间的所有分配格

Middle orders: all distributive lattices between weak and Bruhat

本文研究Coxeter群中位于弱序与Bruhat序之间的分配格（称为中间序），在A型中通过二叉树构造了所有这样的格，并推广到其他Weyl群得到“极小中间序”。

Torus 作用在紧化辫子簇上以及子词复形的多面体性

Torus actions on compactified braid varieties and polytopality of subword complexes

本文证明简单李群辫子簇的簇膨胀作用可延拓至砖紧化，并由此得出闭 Richardson 簇的环面忠实作用及辫子簇为环面的充要条件，进而通过双根自由词为子词复形的多面体性提供新方法并分类相关 Bruhat 区间。