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arXiv · 2508.11543

Combinatorial Methods in Bootstrap Percolation Problems

Gábor V. Nagy·Ákos Süli
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Abstract

An elegant bootstrap percolation result on the hyperrectangle graph was proved by Balogh, Bollobás, 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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Gábor V. Nagy, Ákos Süli. 2025-08-15. Combinatorial Methods in Bootstrap Percolation Problems. https://arxiv.org/abs/2508.11543

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