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Bootstrap percolation on a generalized Hamming cube

2024/12/30 by Zhu, Fengxing
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.20982

Abstract

We consider the r-neighbor bootstrap percolation process on the graph with vertex set V=\0,1\n and edges connecting the pairs at Hamming distance 1,2,…,k, where k≥ 2. We find asymptotics of the critical probability of percolation for r=2,3. In the deterministic setting, we obtain several results for the size of the smallest percolating set for k≥ 2.

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