Maximum Percolation Time on the q-ary Hypercube
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913850550386688 |
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| author | Zhu, Fengxing |
| author_facet | Zhu, Fengxing |
| contents | 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 $q \geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Percolation Time on the q-ary Hypercube Zhu, Fengxing Combinatorics 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 $q \geq 3$. |
| title | Maximum Percolation Time on the q-ary Hypercube |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.00990 |