Twenty-Vertex Model with Domain Wall Boundaries and Domino Tilings
| Autor: | Philippe Di Francesco, Emmanuel Guitter |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, Department of Mathematics, Illinois State University, Illinois State University, ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
| Rok vydání: | 2020 |
| Předmět: |
MSC: 05B45
05A15 82B20 82B23 Root of unity Generalization Alternation (geometry) FOS: Physical sciences Type (model theory) Domino Square (algebra) Theoretical Computer Science Combinatorics [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] Vertex model FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Hexagonal lattice Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics Mathematics::Combinatorics Statistical Mechanics (cond-mat.stat-mech) Applied Mathematics Mathematical Physics (math-ph) Computational Theory and Mathematics Combinatorics (math.CO) Geometry and Topology |
| Zdroj: | The Electronic Journal of Combinatorics The Electronic Journal of Combinatorics, Open Journal Systems, 2020, 27 (2), pp.P2.13. ⟨10.37236/8809⟩ The Electronic Journal of Combinatorics, 2020, 27 (2), pp.P2.13. ⟨10.37236/8809⟩ |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/8809 |
| Popis: | 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. Comment: 63 pages, 22+16 figures |
| Databáze: | OpenAIRE |
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