Double Aztec rectangles

Tri Lai

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We investigate the connection between lozenge tilings and domino tilings by introducing a new family of regions obtained by attaching two different Aztec rectangles. We prove a simple product formula for the generating functions of the tilings of the new regions, which involves the statistics as in the Aztec diamond theorem (Elkies et al. (1992) [2,3]). Moreover, we consider the connection between the generating function and MacMahon's q-enumeration of plane partitions fitting in a given box.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalAdvances in Applied Mathematics
Volume75
DOIs
StatePublished - Apr 1 2016

Keywords

  • Domino tilings
  • Lozenge tilings
  • Perfect matchings
  • Plane partitions
  • Urban renewal

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