# Inverting the Kasteleyn matrix for holey hexagons

@article{Gilmore2017InvertingTK, title={Inverting the Kasteleyn matrix for holey hexagons}, author={Tomack Gilmore}, journal={arXiv: Combinatorics}, year={2017} }

Consider a semi-regular hexagon on the triangular lattice (that is, the lattice consisting of unit equilateral triangles, drawn so that one family of lines is vertical). Rhombus (or lozenge) tilings of this region may be represented in at least two very different ways: as families of non-intersecting lattice paths; or alternatively as perfect matchings of a certain sub-graph of the hexagonal lattice. In this article we show how the lattice path representation of tilings may be utilised in order… Expand

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Lozenge Tiling Function Ratios for Hexagons with Dents on Two Sides

- Mathematics, Computer Science
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- 2020

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… Expand

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