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 of the author and Guitter. 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 Lindström-Gessel-Viennot determinant for the domino tiling problem. The common number of configurations is conjectured to be 2n(n−1)/2 ∏ n−1 (4j+2)! j=0 (n+2j+1)! = 1, 4, 60, 3328, 678912 …. The enumeration result is extended to include refinements of both numbers.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics