Geodesic
Lozenge tilings of a halved hexagon with an array of triangles removed from the boundary. II
Tri Lai1
1Department of Mathematics, University of Nebraska -Lincoln
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later extended this tiling enumeration to a halved hexagon with a triangle cut off from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of triangles has been removed from the staircase side of the halved hexagon. Our result also implies an explicit formula for the number of tilings of a hexagon with an array of triangles removed perpendicularly to the symmetry axis.
DOI : 10.37236/7502
Classification : 05A15, 05B45, 05C30
Mots-clés : perfect matching, plane partition, lozenge tiling, dual graph, graphical condensation

Tri Lai  1

1 Department of Mathematics, University of Nebraska -Lincoln 
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     author = {Tri Lai},
     title = {Lozenge tilings of a halved hexagon with an array of triangles removed from the boundary. {II}},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {4},
     doi = {10.37236/7502},
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Tri Lai. Lozenge tilings of a halved hexagon with an array of triangles removed from the boundary. II. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7502

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