Geodesic
Queens in exile: non-attacking queens on infinite chess boards
F. Michel Dekking1 ; Jeffrey Shallit2 ; N. J. A. Sloane3
1Applied Mathematics (DIAM), Delft University of Technology
2School of Computer Science, University of Waterloo
3OEIS Foundation Inc
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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Number the cells of a (possibly infinite) chessboard in some way with the numbers $0, 1, 2, \ldots$. Consider the cells in order, placing a queen in a cell if and only if it would not attack any earlier queen. The problem is to determine the positions of the queens. We study the problem for a doubly-infinite chessboard of size $\mathbb{Z} \times \mathbb{Z}$ numbered along a square spiral, and an infinite single-quadrant chessboard (of size $\mathbb{N} \times \mathbb{N}$) numbered along antidiagonals. We give a fairly complete solution in the first case, based on the Tribonacci word. There are connections with combinatorial games.
DOI : 10.37236/8905
Classification : 91A46
Mots-clés : Tribonacci word, Tribonacci representation, greedy queens, Wythoff Nim, combinatorial games, Sprague-Grundy function

F. Michel Dekking  1   ; Jeffrey Shallit  2   ; N. J. A. Sloane  3

1 Applied Mathematics (DIAM), Delft University of Technology
2 School of Computer Science, University of Waterloo
3 OEIS Foundation Inc 
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     author = {F. Michel Dekking and Jeffrey Shallit and N. J. A. Sloane},
     title = {Queens in exile: non-attacking queens on infinite chess boards},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {1},
     doi = {10.37236/8905},
     zbl = {1435.91038},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8905/}
}
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F. Michel Dekking; Jeffrey Shallit; N. J. A. Sloane. Queens in exile: non-attacking queens on infinite chess boards. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8905

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