Weak Bruhat order on the set of faces of the permutahedra

子模函数、广义排列多面体、一致预序与余作用双代数

Submodular functions, generalized permutahedra, conforming preorders, and cointeracting bialgebras

本文建立子模函数与广义排列多面体的面与一致预序的一一对应，并利用余作用双代数理论为每个子模函数构造典范多项式。

扩展广义排列多面体与共作用双代数

Extended generalized permutahedra, and cointeracting bialgebras

研究扩展广义排列多面体上共作用双代数结构，通过测量代数框架找到合适共作用概念，证明EGP和仿射锥EGP形成共作用双幺半群，明确其与扩展次模函数对应关系及面和切锥的次模函数，辫子扇等起关键作用。

列举多面体的面

Listing faces of polytopes

本文提出了一种高效算法，用于构造多面体的面哈密顿回路，解决了B-排列多面体的面哈密顿回路猜想。

$s$-弱序与$s$-置换多面体 II：纯区间的组合复形

The $s$-weak order and $s$-permutahedra II: The combinatorial complex of pure intervals

本文为$s$-置换多面体和$s$-结合多面体建立几何基础，证明其为组合复形，给出面计数结果，并提出多面体性猜想及推广方向。

W-Associahedra are In-Your-Face

We use a projection argument to uniformly prove that $W$-permutahedra and $W$-associahedra have the property that if $v,v'$ are two vertices on the same face $f$, then any geodesic between $v$ and $v'$ does not leave $f$. In type $A$, we show that our geometric projection recovers a slight modification of the combinatorial projection given by D. Sleator, R. Tarjan, and W. Thurston.

Counting weighted maximal chains in the circular Bruhat order

The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subset of the real Grassmannian $\mathrm{Gr}(k,n)$ consisting of points with all nonnegative Plücker coordinates. The circular Bruhat order is a poset isomorphic to the face poset of A. Postnikov's (2005) positroid cell decomposition of $\mathrm{Gr}(k,n)_{\geq0}$. We provide a closed formula for the sum of its weighted chains in the spirit of J. Stembridge (2002).