Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2404.18237 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- Define a queen on $\mathbb{Z}_n^d$ with admissible moves parallel to $\mathbf{x}\in\{-1,0,1\}^d$ at arbitrary length. How many queens can be placed on $\mathbb{Z}_n^d$ without any two in conflict? In two dimensions, this problem was initiated by Pólya in 1918 and resolved by Monsky in 1989. We give the first known results in $d$ dimensions, showing that the trivial upper bound $n^{d-1}$ cannot be attained if $n$ is a multiple of $5$, not $25$. We demonstrate, for every $d$, how $n^{d-1}-O(n^{d-2})$ queens can be placed independently.