Lectures on Random Lozenge Tilings

2021 ◽  
Author(s):  
Vadim Gorin
Keyword(s):  
Lozenge Tilings

scholarly journals Enumeration of Hybrid Domino-Lozenge Tilings II: Quasi-Octagonal Regions

10.37236/4669 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Tri Lai
Keyword(s):  
Product Formula ◽  
Cambridge University ◽  
Replacement Method ◽  
Lozenge Tilings ◽  
Simple Product ◽  
Geometric Combinatorics

We use the subgraph replacement method to prove a simple product formula for the tilings of an  8-vertex counterpart of Propp's quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.

scholarly journals Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

10.37236/9363 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Daniel Condon
Keyword(s):  
Triangular Lattice ◽  
Lozenge Tilings ◽  
Simple Product ◽  
Two Sides ◽  
Product Formulas

We give a formula for the number of lozenge tilings of a hexagon on the triangular lattice with unit triangles removed from arbitrary positions along two non-adjacent, non-opposite sides. Our formula implies that for certain families of such regions, the ratios of their numbers of tilings are given by simple product formulas.

scholarly journals Cyclically symmetric lozenge tilings of a hexagon with four holes

2018 ◽  
Vol 96 ◽  
pp. 249-285 ◽  
Author(s):  
Tri Lai ◽  
Ranjan Rohatgi
Keyword(s):  
Lozenge Tilings

scholarly journals Enumeration of Lozenge Tilings of Hexagons with Cut-Off Corners

2002 ◽  
Vol 100 (2) ◽  
pp. 201-231 ◽  
Author(s):  
Mihai Ciucu ◽  
Christian Krattenthaler
Keyword(s):  
Lozenge Tilings
Sign in / Sign up

Export Citation Format

Share Document