S. Corteel, F. Huang and
Christian Krattenthaler
Domino tilings of generalized Aztec triangles
(40 pages)
Abstract.
Di Francesco [Electron. J. Combin. 28.4 (2021), Paper No. 4.38]
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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