Homology of polyomino tilings on flat surfaces
Combinatorics
2021-03-09 v1 Geometric Topology
Abstract
The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a `coloring proof' of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.
Cite
@article{arxiv.2103.04404,
title = {Homology of polyomino tilings on flat surfaces},
author = {Edin Lidjan and Djordje Baralic},
journal= {arXiv preprint arXiv:2103.04404},
year = {2021}
}
Comments
18 pages, 16 figures