Queens in exile: non-attacking queens on infinite chess boards
Combinatorics
2019-07-30 v2
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 x Z numbered along a square spiral, and an infinite single-quadrant chessboard (of size N x 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.
Keywords
Cite
@article{arxiv.1907.09120,
title = {Queens in exile: non-attacking queens on infinite chess boards},
author = {F. Michel Dekking and Jeffrey Shallit and N. J. A. Sloane},
journal= {arXiv preprint arXiv:1907.09120},
year = {2019}
}
Comments
28 pages, 6 figures, 6 tables (V2: Added reference to earlier work on X,Y,M,P sequences. Minor improvements to wording and punctuation.)