Tiling Enumeration of Hexagons with Off-central Holes
Abstract
In the prequel of the paper (arXiv:1803.02792), we considered exact enumerations of the cored versions of a doubly-intruded hexagon. The result generalized Ciucu's work about -cored hexagons (Adv. Math. 2017). In this paper, we provide an extensive list of 30 tiling enumerations of hexagons with three collinear chains of triangular holes with alternating orientations. Besides two chains of holes attaching to the boundary of the hexagon, we remove one more chain of triangles that is slightly off the center of the hexagon. Two of our enumerations imply two conjectures posed by Ciucu, Eisenk\"{o}lbl, Krattenthaler, and Zare (J. Combin. Theory Ser. A 2001) as two very special cases.
Keywords
Cite
@article{arxiv.1905.07119,
title = {Tiling Enumeration of Hexagons with Off-central Holes},
author = {Tri Lai},
journal= {arXiv preprint arXiv:1905.07119},
year = {2019}
}
Comments
This is roughly the second half of arXiv:1803.02792, which is titled "Lozenge Tilings of Hexagons with Central Holes and Dents ". The contents of this paper will be removed from arXiv:1803.02792