The problem of the pawns
| dc.creator | Kitaev, S. | |
| dc.creator | Mansour, T. | |
| dc.date | 2003-05-18 | |
| dc.date.accessioned | 2026-07-07T04:58:05Z | |
| dc.date.available | 2026-07-07T04:58:05Z | |
| dc.description | In this paper we study the number $M_{m,n}$ of ways to place nonattacking pawns on an $m\times n$ chessboard. We find an upper bound for $M_{m,n}$ and analyse its asymptotic behavior. It turns out that $\lim_{m,n\to\infty}(M_{m,n})^{1/mn}$ exists and is bounded from above by $(1+\sqrt{5})/2$. Also, we consider a lower bound for $M_{m,n}$ by reducing this problem to that of tiling an $(m+1)\times (n+1)$ board with square tiles of size $1\times 1$ and $2\times 2$. Moreover, we use the transfer-matrix method to implement an algorithm that allows us to get an explicit formula for $M_{m,n}$ for given $m$. | |
| dc.description | 16 pages; 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0305253 | |
| dc.identifier | http://arxiv.org/abs/math/0305253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67497 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16; 05C05; 52C20; 82B20 | |
| dc.title | The problem of the pawns | |
| dc.type | text |