随机Steiner系统与各维有界度上边界扩张
Random Steiner systems and bounded degree coboundary expanders of every dimension
摘要：
本文引入了一个新的随机$d$ -维单纯复形模型，对于$d\geq 2$，其$(d-1)$ -胞元具有有界度.我们发现，以高概率，根据这个模型采样的复合物是共边界扩展。该结构依赖于Keevash最近的设计结果[Ke 14]，扩展的证明使用了Evra和Kaufman在[EK 15]中开发的技术。这给出了在[DK 12]中提出的问题的完整解，该问题在二维情况下由Lubotzky和Meshulam [LM 13]解决。
英文摘要：
We introduce a new model of random $d$-dimensional simplicial complexes, for $d\geq 2$, whose $(d-1)$-cells have bounded degrees. We show that with high probability, complexes sampled according to this model are coboundary expanders. The construction relies on Keevash's recent result on designs [Ke14], and the proof of the expansion uses techniques developed by Evra and Kaufman in [EK15]. This gives a full solution to a question raised in [DK12], which was solved in the two-dimensional case by Lubotzky and Meshulam [LM13].
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。
