Abstract
Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, … . 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 ℤ × ℤ numbered along a square spiral, and an infinite single-quadrant chessboard (of size N × 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.
Original language | English |
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Article number | P1.52 |
Pages (from-to) | 1-27 |
Number of pages | 27 |
Journal | Electronic Journal of Combinatorics |
Volume | 27 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Combinatorial games
- Greedy Queens
- Sprague-Grundy function
- Tribonacci representation
- Tribonacci word
- Wythoff Nim