近似图着色与晶体
Approximate Graph Colouring and Crystals
摘要：
我们表明，近似图着色没有解决任何级别的仿射整数规划（AIP）的层次。为了建立结果，我们将展示一个欺骗AIP层次的图形的问题转化为构建高度对称的晶体张量的问题。为了证明任意维晶体的存在，我们提供了一个可实现的张量系统的组合特征;即，低维张量的集合，可以实现为单个高维张量的投影。
英文摘要：
We show that approximate graph colouring is not solved by any level of the affine integer programming (AIP) hierarchy. To establish the result, we translate the problem of exhibiting a graph fooling a level of the AIP hierarchy into the problem of constructing a highly symmetric crystal tensor. In order to prove the existence of crystals in arbitrary dimension, we provide a combinatorial characterisation for realisable systems of tensors; i.e., sets of low-dimensional tensors that can be realised as the projections of a single high-dimensional tensor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
