Geodesic
Holey Matrimony: Marrying Two Approaches to a Tiling Problem
Séminaire lotharingien de combinatoire, 78B (2017)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/}
}
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AU  - Tomack Gilmore
TI  - Holey Matrimony: Marrying Two Approaches to a Tiling Problem
JO  - Séminaire lotharingien de combinatoire
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VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a25/
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%T Holey Matrimony: Marrying Two Approaches to a Tiling Problem
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%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/