Tiling Parity Results and the Holey Square Solution

2004/09/07 by Bridget Eileen Tenner, Tenner, Bridget Eileen
Mathematics · #05B45 #05C70 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B45 #msc:05C70

paper · pdf · doi:10.48550/arxiv.math/0409105

12 pages. Generalized parity theorem and new corollaries

arxiv created 2004/10/07 · arxiv updated 2009/12/01

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.

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