Geodesic
The problem of kings
The electronic journal of combinatorics, Tome 2 (1995)
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Let $f(n)$ denote the number of configurations of $n^2$ mutually non-attacking kings on a $2n\times 2n$ chessboard. We show that $\log f(n)$ grows like $2n\log n - 2n\log 2$, with an error term of $O(n^{4/5}\log n)$. The result depends on an estimate for the sum of the entries of a high power of a matrix with positive entries.
DOI : 10.37236/1212
Classification : 05A15, 05B30, 91A99, 05A10
Mots-clés : number of configurations, kings, chessboard, matrix 
@article{10_37236_1212,
     author = {Michael Larsen},
     title = {The problem of kings},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1212},
     zbl = {0827.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1212/}
}
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Michael Larsen. The problem of kings. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1212

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