1DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ILLINOIS, URBANA, IL 61821, U.S.A. AND INSTITUT DE PHYSIQUE THÉORIQUE, UNIVERSITÉ PARIS SACLAY, CEA, CNRS, F-91191 GIF-SUR-YVETTE, FRANCE
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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.
1
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ILLINOIS, URBANA, IL 61821, U.S.A. AND INSTITUT DE PHYSIQUE THÉORIQUE, UNIVERSITÉ PARIS SACLAY, CEA, CNRS, F-91191 GIF-SUR-YVETTE, FRANCE
@article{10_37236_8809,
author = {Philippe Di Francesco and Emmanuel Guitter},
title = {Twenty-vertex model with domain wall boundaries and domino tilings},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/8809},
zbl = {1439.05047},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8809/}
}
TY - JOUR
AU - Philippe Di Francesco
AU - Emmanuel Guitter
TI - Twenty-vertex model with domain wall boundaries and domino tilings
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/8809/
DO - 10.37236/8809
ID - 10_37236_8809
ER -
%0 Journal Article
%A Philippe Di Francesco
%A Emmanuel Guitter
%T Twenty-vertex model with domain wall boundaries and domino tilings
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/8809/
%R 10.37236/8809
%F 10_37236_8809
Philippe Di Francesco; Emmanuel Guitter. Twenty-vertex model with domain wall boundaries and domino tilings. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8809
