On the realization space of the cube

半立方体图在半自旋Grassmannian中的等距嵌入

Isometric embeddings of half-cube graphs in half-spin Grassmannians

设$Π$是$\textsf{D}_{n}$型的极空间。用${\mathcal G}_δ(Π)$、$δ\in \{+,-\}$表示相关的半自旋格拉斯曼图，并将相应的半自旋格拉斯曼图写成$Γ_δ(Π)$。当$n\ge 4$为偶数时，${\mathcal G}_δ(Π)$的单元将被刻画为半立方体图$\frac{1}{2}H_n$在$Γ_δ(Π)$中的等距嵌入的像.作为应用，在$n\ge 6$是偶数的假设下，我们描述了与$\textsf{D}_{n'}$型极空间相关的半自旋Grassmann图中$Γ_δ(Π)$的所有等距嵌入.

The diagonal of the associahedra

This paper introduces a new method to solve the problem of the approximation of the diagonal for face-coherent families of polytopes. We recover the classical cases of the simplices and the cubes and we solve it for the associahedra, also known as Stasheff polytopes. We show that it satisfies an easy-to-state cellular formula. For the first time, we endow a family of realizations of the associahedra (the Loday realizations) with a topological and cellular operad structure; it is shown to be compatible with the diagonal maps.

复曲面立方体

Toric Cubes

复曲面立方体是由二项式不等式定义的标准立方体的子集。这些基本的半代数集合正是标准立方体在单项式映射下的映象。我们从拓扑组合学的角度研究复曲面立方体。作为CW-复形的显式分解被构造。它们的开胞是复曲面立方体的内部，它们的边界是子复形。环面立方体的激励性例子是遗传学中的边积空间，我们的工作推广了该空间的已知结果。

立方与广义实Bott流形

Cubes and Generalized Real Bott Manifolds

本文定义了一个带角流形上的面对结构及其封闭空间的概念。我们将详细研究任意立方体上的面对结构，并研究立方体上的面对结构的封闭空间何时是闭流形。特别地，对于任何在维度n中具有零对角的二元方阵$A$，在n维立方体上存在规范的面配对结构$F_A$。我们将证明，我们可以从这样的$F_A$的密封空间中得到的所有闭流形既不大于也不小于所有的广义实Bott流形--由Choi，Masuda和Suh引入的一类特殊的实环面流形。

超越树：加权汉明立方体子集的度量几何

Beyond trees: the metric geometry of subsets of weighted Hamming cubes

本文研究加权汉明立方体子集的度量几何，揭示其关联几何量间的意外关系，推导距离矩阵行列式等公式，拓展此前的树与标准汉明立方体相关结果，并刻画其中的非平凡1-多边形等式。

Tilings of $(2\times2\times n)$-board with colored cubes and bricks

Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of the tilings of an $n$-long board considering the $(n-1)$-long board. It describes recursively the number of possible breakable and unbreakable tilings. Finally, we give some identities for the recursions using breakability. The method of determining the recur…