Independent sets in the middle two layers of Boolean lattice
Independent sets in the middle two layers of Boolean lattice
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DOI：
10.1016/j.jcta.2020.105341
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
J. Balogh;Ramon Garcia;Lina Li
中科院分区：
文献类型：
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作者：
J. Balogh;Ramon Garcia;Lina Li
对于奇数n= 2 d− 1，设B（n，d）是超立方体Q n的由两个最大层导出的子图。本文描述了B（n，d）中独立集的典型结构，并给出了独立集个数的精确渐近性。证明使用Sapozhenko的图容器方法和最近开发的方法的詹森和帕金斯，它结合了Sapozhenko的图容器引理与集群扩展的聚合物模型从统计物理。
For an odd integer n= 2 d− 1, let B (n, d) be the subgraph of the hypercube Q n induced by the two largest layers. In this paper, we describe the typical structure of independent sets in B (n, d) and give precise asymptotics on the number of them. The proofs use Sapozhenko's graph container method and a recently developed method of Jenssen and Perkins, which combines Sapozhenko's graph container lemma with the cluster expansion for polymer models from statistical physics.