通过分拆的内蕴覆盖研究对称群上的Bruhat序

Wachs permutations, Bruhat order and weak order

We study the partial orders induced on Wachs and signed Wachs permutations by the Bruhat and weak orders of the symmetric and hyperoctahedral groups. We show that these orders are graded, determine their rank function, characterize their ordering and covering relations, and compute their characteristic polynomials, when partially ordered by Bruhat order, and determine their structure explicitly when partially ordered by right weak order.

Homotopy type of intervals of the second higher Bruhat orders

The higher Bruhat order is a poset of cubical tilings of a cyclic zonotope whose covering relations are cubical flips. For a 2-dimensional zonotope, the higher Bruhat order is isomorphic to a poset on commutation classes of reduced words for the longest element of a type A Coxeter system. For this case, we prove that the noncontractible intervals are in natural correspondence with the zonogonal tilings of a zonogon. Our proof uses some tools developed by Felsner and Weil to show that the two standard orderings on the rhombic tilings of a zonogon are identical.

交换类的简化解和更高布里哈特序在仿射排列中的应用

Commutation classes of reduced words and higher Bruhat orders for affine permutations

本文研究了仿射排列中交换类的简化解和更高布里哈特序的结构，提出了一种推广弱序区间[ id, w ]的通用方法，揭示了交换类与布里哈特序之间的关系。

酿造 Fubini-Bruhat 序

Brewing Fubini-Bruhat Orders

本文围绕生成线构型子簇，提出并研究三种由 Fubini 词索引的偏序——低因序、中焙序和浓缩序，推广了排列上的弱序与 Bruhat 序，并探讨了 Schubert 簇性质在这些新序中的延伸。

拉丁方和交错符号超矩阵的Bruhat序

A Bruhat order for Latin squares and alternating sign hypermatrices

本文定义了拉丁方和交错符号超矩阵上的Bruhat序，通过角点和超矩阵的逐点支配关系刻画该序，并证明了角点和超矩阵构成分配格，但不同于二维情形，它不是拉丁方偏序集的Dedekind-MacNeille完备化。

Enumerative properties of restricted words and compositions

In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count cyclically restricted and circular objects. This either fills gaps in the current literature by e.g. considering particular new patterns, or involves general progress, notably with locally restricted compositions over a finite group. We associate these compositions to walks on a covering graph whose structure is exploited to simplify asymptotic expressions. Specifica…