Geodesic
Lozenge tilings of hexagons with central holes and dents
Tri Lai1
1University of Nebraska - Lincoln
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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Ciucu proved a simple product formula for the tiling number of a hexagon in which a chain of equilateral triangles of alternating orientations, called a `fern', has been removed from the center (Adv. Math. 2017). In this paper, we present a multi-parameter generalization of this work by giving an explicit tiling enumeration for a hexagon with three ferns removed, besides the central fern as in Ciucu's region, we remove two new ferns from two sides of the hexagon. Our result also implies a new `dual' of MacMahon's classical formula of boxed plane partitions, corresponding to the exterior of the union of three disjoint concave polygons obtained by turning 120 degrees after drawing each side.
DOI : 10.37236/8716
Classification : 05B45, 05A15, 05C30, 05A18, 52C20
Mots-clés : perfect matchings, plane partitions, lozenge tilings, dual graph, graphical condensation

Tri Lai  1

1 University of Nebraska - Lincoln 
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     title = {Lozenge tilings of hexagons with central holes and dents},
     journal = {The electronic journal of combinatorics},
     year = {2020},
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     number = {1},
     doi = {10.37236/8716},
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Tri Lai. Lozenge tilings of hexagons with central holes and dents. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8716

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