Tiling Parity Results and the Holey Square Solution

Details Tiling Parity Results and the Holey Square Solution Tiling Parity Results and the Holey Square Solution

2004-09-07

arxiv.org/abs/math/0409105v2

Mathematics

Combinatorics

12 pages. Generalized parity theorem and new corollaries

Scientific paper

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.

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