半格的分配格覆盖

对称 Fibonacci 分配格与特殊线性李代数的表示

Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras

本文构造一族秩对称、菱形着色的 Fibonacci 分配格，统一已有格结构，并用其自然实现特殊线性李代数表示及具有极值性质的权基。

Distributive lattices and Auslander regular algebras

Let $L$ denote a finite lattice with at least two points and let $A$ denote the incidence algebra of $L$. We prove that $L$ is distributive if and only if $A$ is an Auslander regular ring, which gives a homological characterisation of distributive lattices. In this case, $A$ has an explicit minimal injective coresolution, whose $i$-th term is given by the elements of $L$ covered by precisely $i$ elements. We give a combinatorial formula of the Bass numbers of $A$. We apply our results to show that the order dimension of a distributive lattice $L$ coincides with the global dimension of the inci…

超晶格与δ键

ULD-Lattices and Delta-Bonds

利用覆盖图的边着色刻画了上局部分配格（ULD-格）。在许多情况下，一组组合对象带有格的序结构，这个特征给出了分配性或UL-分配性的巧妙证明。这是通过证明一个分配格结构的Delta键不变的循环流差。这个例子概括了几个以前研究的晶格结构，特别是c-取向（Propp），α-取向的可平面图（Felsner，resp. de Mendez）和平面流（Khuller、Naor和Klein）。这一特征也适用于其他情况，例如掷筹码游戏。

有限偏序集的两个覆盖多项式及其在根系和ad-幂零理想中的应用

Two covering polynomials of a finite poset, with applications to root systems and ad-nilpotent ideals

我们引入了两个多项式（在$q$中）与有限偏序集$P$相关联，它们编码了$P$中覆盖关系的一些信息。若$P$是分配格，则$P$同构于偏序集$L$中的对偶阶理想的偏序集，则这些多项式重合，且$q$的系数等于$L$中$k$ -元反链的个数.一般来说，这两个覆盖多项式是不同的，我们引入一个偏差多项式$P$，它衡量这两者之间的差异。然后，我们计算所有这些多项式的情况下，其中$P$是一个偏序集与不可约根系。这些是1）正根的偏序集，2）ad-幂零理想理想的偏序集，3）阿贝尔理想的偏序集。

横贯格

Transversal Lattices

本文研究循环平集格对应拟阵必为横贯拟阵的 Tr-格，给出其充分条件、必要条件及由已知 Tr-格构造新格的方法。

格中局部分配性度量的Rises

Rises for Measuring Local Distributivity in Lattices

本文引入了格中rises的概念来度量局部分配性，证明了格分配性与非单位rises的等价关系，并揭示了真实数据概念格高度并分配但弱交分配的特性。

Flip distances between graph orientations

Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in triangulations of a convex polygon. For some definition of a flip graph, a natural computational problem to consider is the flip distance: Given two objects, what is the minimum number of flips needed to transform one into the other? We consider flip graphs on orientations of simple graphs, where flips consist of reversing the direction of some edges. More precisely,…