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arXiv · 2305.01774

Domino tilings of generalized Aztec triangles

Sylvie Corteel·Frederick Huang·Christian Krattenthaler
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Abstract

Di Francesco introduced Aztec triangles as combinatorial objects for which their domino tilings are equinumerous with certain sets of configurations of the twenty-vertex model that are the main focus of his article. We generalize Di Francesco's construction of Aztec triangles. While we do not know whether there is again a correspondence with configurations in the twenty-vertex model, we prove closed-form product formulas for the number of domino tilings of our generalized Aztec triangles. As a special case, we obtain a proof of Di Francesco's conjectured formula for the number of domino tilings of his Aztec triangles, and thus for the number of the corresponding configurations in the twenty-vertex model.

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Sylvie Corteel, Frederick Huang, Christian Krattenthaler. 2023-05-02. Domino tilings of generalized Aztec triangles. https://arxiv.org/abs/2305.01774

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