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Domino Tilings of Shifted Two-Block Regions: Exact Identities, Equal-Height Theorems, and Computational Evidence

We study domino tilings of a rectangle and of a natural family of shifted two-block regions. A seam decomposition gives an exact identity for the difference between the rectangular tiling count and the shifted count. We prove, in particular, that every nontrivially shifted equal-...

Domino Tilings of Shifted Two-Block Regions: Exact Identities, Equal-Height Theorems, and Computational Evidence

We study domino tilings of a rectangle and of a natural family of shifted two-block regions. A seam decomposition gives an exact identity for the difference between the rectangular tiling count and the shifted count. We prove, in particular, that every nontrivially shifted equal-...