Elsevier

Discrete Mathematics

Volume 338, Issue 11, 6 November 2015, Pages 1866-1872
Discrete Mathematics

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

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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”.

Keywords

Tilings
Perfect matchings
Plane partitions
Graphical condensation

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