Tiling Parity Results and the Holey Square Solution
Combinatorics
2007-05-23 v2
Abstract
We prove combinatorially that the parity of the number of domino tilings of a region is equal to the parity of the number of domino tilings of a particular subregion. Using this result we can resolve the holey square conjecture. We furthermore give combinatorial proofs of several other tiling parity results, including that the number of domino tilings of a particular family of rectangles is always odd.
Keywords
Cite
@article{arxiv.math/0409105,
title = {Tiling Parity Results and the Holey Square Solution},
author = {Bridget Eileen Tenner},
journal= {arXiv preprint arXiv:math/0409105},
year = {2007}
}
Comments
12 pages. Generalized parity theorem and new corollaries