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On the number of partitions of the hypercube ${\bf Z}_q^n$ into large subcubesстатья
- Автор: Tarannikov Yuriy
- Сборник: E-print Archive of Cornell University
- Год издания: 2024
- Издательство: Cornell University Press
- Местоположение издательства: United States
- Номер статьи: arXiv:2411.04479
- DOI: 10.48550/ARXIV.2411.04479
- Аннотация: We prove that the number of partitions of the hypercube $Z_q^n$ 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.
- Добавил в систему: Таранников Юрий Валерьевич