TY - JOUR
T1 - Twenty-vertex model with domain wall boundaries and domino tilings
AU - Di Francesco, Philippe
AU - Guitter, Emmanuel
N1 - \u2217Partially supported by the Morris and Gertrude Fine endowment, the NSF grant DMS18-02044 and the Simons Fellowship No 617036. \u2020Supported by the grant ANR-14-CE25-0014 (ANR GRAAL)
Supported by the grant ANR-14-CE25-0014 (ANR GRAAL).
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85085869906&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85085869906&partnerID=8YFLogxK
U2 - 10.37236/8809
DO - 10.37236/8809
M3 - Article
AN - SCOPUS:85085869906
SN - 1077-8926
VL - 27
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 2
M1 - P2.13
ER -