Enumeration of hybrid domino-lozenge tilings

Tri Lai

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We solve and generalize an open problem posted by James Propp (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999) on the number of tilings of quasi-hexagonal regions on the square lattice with every third diagonal drawn in. We also obtain a generalization of Douglas' theorem on the number of tilings of a family of regions of the square lattice with every second diagonal drawn in.

Original languageEnglish (US)
Pages (from-to)53-81
Number of pages29
JournalJournal of Combinatorial Theory. Series A
Volume122
Issue number1
DOIs
StatePublished - Feb 1 2014

Keywords

  • Aztec diamonds
  • Aztec rectangles
  • Dual graphs
  • Perfect matchings
  • Quasi-hexagons
  • Tilings

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