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Journal articles
Twenty-Vertex Model with Domain Wall Boundaries and Domino Tilings
Abstract : We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an Aztec-like holey square, with a central cross-shaped hole. The proof of this statement makes extensive use of integrability and of a connection to the 6-Vertex model. The type 3 configurations are conjectured to be in same number as domino tilings of a particular triangle. The four enumeration problems are reformulated in terms of four types of Alternating Phase Matrices with entries 0 and sixth roots of unity, subject to suitable alternation conditions. Our result is a generalization of the ASM-DPP correspondence. Several refined versions of the above correspondences are also discussed.
Cited literature [39 references]
https://hal-cea.archives-ouvertes.fr/cea-02932251
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, September 8, 2020 - 9:59:51 AM
Last modification on : Tuesday, December 8, 2020 - 9:47:35 AM
Long-term archiving on: : Friday, December 4, 2020 - 5:26:31 PM
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, September 8, 2020 - 9:59:51 AM
Last modification on : Tuesday, December 8, 2020 - 9:47:35 AM
Long-term archiving on: : Friday, December 4, 2020 - 5:26:31 PM
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