Maximum Percolation Time on the q-ary Hypercube

Abstract

We consider the $2$-neighbor bootstrap percolation process on the $n$-dimensional $q$-ary hypercube with vertex set $V=\{0,1,\dots ,q-1{\}}^n$ and edges connecting the pairs at Hamming distance $1$. We extend the main theorem of Przykucki(2012) about the maximum percolation time with threshold $r=2$ on the binary hypercube to the $q$-ary case, finding the exact value of this time for all $q\ge 3$.