A generalization of Aztec diamond theorem, part I

Tri Lai

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas' theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schr̈oder paths, then applying Lindstr̈om-Gessel-Viennot methodology.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume21
Issue number1
DOIs
StatePublished - Mar 10 2014
Externally publishedYes

Keywords

  • Aztec diamonds
  • Dominos
  • Perfect matchings
  • Schröder paths
  • Tilings

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