论文标题
一系列复合体的确定性着色
Deterministic coloring of a family of complexes
论文作者
论文摘要
这是第二张专门用于构建有限呈现的无限零半群的纸质，具有身份$ x^9 = 0 $。该构建回答了Lev Shevrin和Mark Sapir的问题。在第一部分中，我们构建了具有一组属性的复合物序列。也就是说，所有这些复合物都是均匀的椭圆形：任何两个点$ a $ a $ a $ a $ a $ a $ d $都可以与最短路径的系统相连，形成宽度$λ\ cdot d $的磁盘，对于某些全球常数$λ> 0 $。在证明的第二部分中，引入了具有确定性的有限颜色系统：对于该复合物组成的每个最小正方形，三个角度的颜色决定了第四个角的颜色。本文专门用于证明的第二部分。
This is the second paper devoted to construction of finitely presented infinite nil semigroup with identity $x^9=0$. This construction answers to the problem of Lev Shevrin and Mark Sapir. In the first part we constructed the sequence of complexes with some set of properties. Namely, all these complexes are uniform elliptic: any two points $A$ and $B$ with distance $d$ can be connected with a system of shortest paths forming a disk of width $ λ\cdot D $ for some global constant $ λ> 0 $. In the second part of the proof, a finite system of colors with determinism is introduced: for each minimum square that the complex consists of, the color of the three angles determines the color of the fourth corner. The present paper is devoted to the second part of the proof.
