论文标题
使用锯齿ZAG产品的高维扩展
High dimensional expansion using zig-zag product
论文作者
论文摘要
我们希望对最新的组合结构进行讨论，这些结构是3-均匀的超图扩展器，以更一般的视角查看它们，从而阐明了与Zig-Zag产品的以前未知的关系。我们通过引入一个称为三重态结构的新结构来做到这一点，该结构在每个顶点周围保持相同的本地环境。在某些情况下，该结构预计会产生一个有界的超图扩展器家族，其二维随机行走会收敛。我们将此处获得的结果应用于几个已知的构造，获得了比以前已知的更好的扩展率。也就是说，我们这样做的是Conlon的建设，以及Chapman，Linal和Peled的$ S = [1,1,0] $构造。
We wish to renew the discussion over recent combinatorial structures that are 3-uniform hypergraph expanders, viewing them in a more general perspective, shedding light on a previously unknown relation to the zig-zag product. We do so by introducing a new structure called triplet structure, that maintains the same local environment around each vertex. The structure is expected to yield, in some cases, a bounded family of hypergraph expanders whose 2-dimensional random walk converges. We have applied the results obtained here to several known constructions, obtaining a better expansion rate than previously known. Namely, we did so in the case of Conlon's construction and the $S=[1,1,0]$ construction by Chapman, Linal and Peled.
