Twenty vertex model and domino tilings of the aztec triangle

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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.

Original languageEnglish (US)
Article numberP4.38
JournalElectronic Journal of Combinatorics
Issue number4
StatePublished - 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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