"Minesweeper" and spectrum of discrete Laplacians
Discrete Mathematics
2010-11-09 v3
Abstract
The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.
Keywords
Cite
@article{arxiv.0806.3480,
title = {"Minesweeper" and spectrum of discrete Laplacians},
author = {Oleg German and Evgeny Lakshtanov},
journal= {arXiv preprint arXiv:0806.3480},
year = {2010}
}
Comments
We add consideration of tables based on the triangle tiling of the plane. Its paper version encounters situations typical for the computer "Minesweeper" game