Combinatorial Methods in Bootstrap Percolation Problems
G\'abor V. Nagy, \'Akos S\"uli
TL;DR
This paper revisits a bootstrap percolation problem on hyperrectangle graphs, providing a purely combinatorial proof for the base case across all dimensions and highlighting open problems for further research.
Contribution
It offers a new combinatorial approach to a known bootstrap percolation problem, extending the understanding of the base case in all dimensions.
Findings
Base case solved for all dimensions
Provides a purely combinatorial proof
Poses open problems for remaining cases
Abstract
An elegant bootstrap percolation result on the hyperrectangle graph was proved by Balogh, Bollob\'as, Morris, and Riordan using a linear algebric method in 2012. This paper studies the same problem by purely combinatorial means. The base case is solved for all dimensions, and we pose open problems for the remaining cases.
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