Line Percolation in Finite Projective Planes

TL;DR

This paper investigates bootstrap percolation in finite projective planes, providing precise results on minimal and maximal percolating sets, percolation time, and critical probability, advancing understanding of percolation dynamics in finite geometries.

Contribution

It offers new sharp bounds and exact results for percolation parameters in finite projective planes, a novel setting in bootstrap percolation research.

Findings

Sharp bounds on minimal percolating sets

Exact results on maximal non-percolating sets

Analysis of percolation time and critical probability

Abstract

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.