On the number of partitions of the hypercube ${\bf Z}_q^n$ into large subcubes
| Autor: | Tarannikov, Yuriy |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Siberian Electronic Mathematical Reports, Volume 21 (2024), N 2, pp. 1503-1521 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.33048/semi.2024.21.096 |
| Popis: | We prove that the number of partitions of the hypercube ${\bf Z}_q^n$ into $q^m$ subcubes of dimension $n-m$ each for fixed $q$, $m$ and growing $n$ is asymptotically equal to $n^{(q^m-1)/(q-1)}$. For the proof, we introduce the operation of the bang of a star matrix and demonstrate that any star matrix, except for a fractal, is expandable under some bang, whereas a fractal remains to be a fractal under any bang. |
| Databáze: | arXiv |
| Externí odkaz: |
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