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- W4287332105 abstract "We show that the number of configurations of the 20 Vertex model on certain domains with domain wall type boundary conditions is equal to the number of domino tilings of Aztec-like triangles, proving a conjecture from [P. Di Francesco and E. Guitter, Twenty-Vertex Model with Domain Wall Boundaries and Domino Tilings, Elec. Jour. of Combinatorics 27 (2020), no. 2, P2.13]. The result is based on the integrability of the 20 Vertex model and uses a connection to the U-turn boundary 6 Vertex model to re-express the number of 20 Vertex configurations as a simple determinant, which is then related to a Lindstrom-Gessel-Viennot determinant for the domino tiling problem. The common number of configurations is conjectured to be $2^{n(n-1)/2}prod_{j=0}^{n-1}frac{(4j+2)!}{(n+2j+1)!}=1, 4, 60, 3328, 678912...$ The enumeration result is extended to include refinements of both numbers." @default.
- W4287332105 created "2022-07-25" @default.
- W4287332105 creator A5046514222 @default.
- W4287332105 date "2021-02-04" @default.
- W4287332105 modified "2023-09-26" @default.
- W4287332105 title "Twenty Vertex model and domino tilings of the Aztec triangle" @default.
- W4287332105 doi "https://doi.org/10.48550/arxiv.2102.02920" @default.
- W4287332105 hasPublicationYear "2021" @default.
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