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Domino tilings of generalized Aztec triangles
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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.
Forward citations
Cited by 2 Pith papers
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The 1/3-phenomenon of placement probabilities of tilings in the semiregular hexagon
Krattenthaler's 1/3-phenomenon for lozenge placement probabilities in semiregular hexagons holds for all fixed positions and side lengths when the hexagon is large enough.
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A short combinatorial proof of Di Francesco's conjecture on Aztec triangles
Byun and Ciucu prove Di Francesco's product formula for Aztec triangle domino tilings via a short combinatorial argument, avoiding the computer calculations of earlier proofs.
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