Geodesic
Holey Matrimony: Marrying Two Approaches to a Tiling Problem
Séminaire lotharingien de combinatoire, 78B (2017) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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Consider an hexagonal region on the triangular lattice, the interior of which contains a number of holes. This extended abstract outlines a recent result by the author that marries together two separate approaches to counting tilings in order to express the number of rhombus tilings of a holey hexagon (subject to very mild restrictions) as a determinant whose size is dependent only on the regions that have been removed. The main result follows from explicitly deriving the (i,j)-entries of the inverse Kasteleyn matrix corresponding to certain sub-graphs of the hexagonal lattice. This generalises a number of known results and may well lead to a proof of Ciucu's electrostatic conjecture for the most general family of holes to date. 

@article{SLC_2017_78B_a25,
     author = {Tomack Gilmore},
     title = {Holey {Matrimony:} {Marrying} {Two} {Approaches} to a {Tiling} {Problem}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/}
}
TY  - JOUR
AU  - Tomack Gilmore
TI  - Holey Matrimony: Marrying Two Approaches to a Tiling Problem
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/
ID  - SLC_2017_78B_a25
ER  - 
%0 Journal Article
%A Tomack Gilmore
%T Holey Matrimony: Marrying Two Approaches to a Tiling Problem
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/
%F SLC_2017_78B_a25
Tomack Gilmore. Holey Matrimony: Marrying Two Approaches to a Tiling Problem. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/