A new proof for the number of lozenge tilings of quartered hexagons

Tri Lai

doi:10.1016/j.disc.2015.04.024

A new proof for the number of lozenge tilings of quartered hexagons

Tri Lai

Institute for Mathematics and its Applications

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our result generalizes a result of Proctor on enumeration of plane partitions contained in a "maximal staircase".

Original language	English (US)
Pages (from-to)	1866-1872
Number of pages	7
Journal	Discrete Mathematics
Volume	338
Issue number	11
DOIs	https://doi.org/10.1016/j.disc.2015.04.024
State	Published - Jun 6 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

Keywords

Graphical condensation
Perfect matchings
Plane partitions
Tilings

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10.1016/j.disc.2015.04.024

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abstract = "It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our result generalizes a result of Proctor on enumeration of plane partitions contained in a {"}maximal staircase{"}.",

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A new proof for the number of lozenge tilings of quartered hexagons

Abstract

Bibliographical note

Keywords

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