Enumeration of antisymmetric monotone triangles and domino tilings of quartered Aztec rectangles

Tri Lai

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In their unpublished work, Jockusch and Propp showed that a 2-enumeration of antisymmetric monotone triangles is given by a simple product formula. On the other hand, the author proved that the same formula counts the domino tilings of the quartered Aztec rectangle. In this paper, we explain this phenomenon directly by building a correspondence between the antisymmetric monotone triangles and domino tilings of the quartered Aztec rectangle.

Original languageEnglish (US)
Pages (from-to)1512-1518
Number of pages7
JournalDiscrete Mathematics
Volume339
Issue number5
DOIs
StatePublished - May 6 2016

Bibliographical note

Funding Information:
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

  • Aztec diamonds
  • Aztec rectangles
  • Domino tilings
  • Monotone triangles

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