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

Tri Lai

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8 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 languageEnglish (US)
Pages (from-to)1866-1872
Number of pages7
JournalDiscrete Mathematics
Volume338
Issue number11
DOIs
StatePublished - Jun 6 2015

Bibliographical note

Funding Information:
The author wants to thank Christian Krattenthaler for helpful comments, and Ranjan Rohatgi for useful discussion. This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation (grant no. DMS-0931945 ).

Keywords

  • Graphical condensation
  • Perfect matchings
  • Plane partitions
  • Tilings

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